Java CUP. Java CUP Specifications. User Code Additions You may define Java code to be included within the generated parser:

Size: px
Start display at page:

Download "Java CUP. Java CUP Specifications. User Code Additions You may define Java code to be included within the generated parser:"

Transcription

1 Jv CUP Jv CUP is prser-genertion tool, similr to Ycc. CUP uilds Jv prser for LALR(1) grmmrs from production rules nd ssocited Jv code frgments. When prticulr production is recognized, its ssocited code frgment is executed (typiclly to uild n AST). CUP genertes Jv source file prser.jv. It contins clss prser, with method Symol prse() The Symol returned y the prser is ssocited with the grmmr s strt symol nd contins the AST for the whole source progrm. The file sym.jv is lso uilt for use with JLex-uilt scnner (so tht oth scnner nd prser use the sme token codes). If n unrecovered syntx error occurs, Exception() is thrown y the prser. CUP nd Ycc ccept exctly the sme clss of grmmrs ll LL(1) grmmrs, plus mny useful non- LL(1) grmmrs. CUP is clled s jv jv_cup.min < file.cup Jv CUP Specifictions User Code Additions You my define Jv code to e included within the generted prser: ction code {: /*jv code */ This code is plced within the generted ction clss (which holds user-specified production ctions). prser code {: /*jv code */ This code is plced within the generted prser clss. init with{: /*jv code */ This code is used to initilize the generted prser. scn with{: /*jv code */ This code is used to tell the generted prser how to get tokens from the scnner. Jv CUP specifictions re of the form: Pckge nd import specifictions User code dditions Terminl nd non-terminl declrtions A context-free grmmr, ugmented with Jv code frgments Pckge nd Import Specifictions You define pckge nme s: pckge nme You dd imports to e used s: import jv_cup.runtime.*

2 Terminl nd Non-terminl Declrtions You define terminl symols you will use s: terminl clssnme nme 1, nme 2,... clssnme is clss used y the scnner for tokens (CSXToken, CSXIdentifierToken, etc.) You define non-terminl symols you will use s: non terminl clssnme nme 1, nme 2,... clssnme is the clss for the AST node ssocited with the non-terminl (stmtnode, exprnode, etc.) Production Rules Production rules re of the form nme ::= nme 1 nme 2... ction or nme ::= nme 1 nme 2... ction 1 nme 3 nme 4... ction 2... Nmes re the nmes of terminls or non-terminls, s declred erlier. Actions re Jv code frgments, of the form {: /*jv code */ The Jv oject ssocted with symol ( token or AST node) my e nmed y dding :id suffix to terminl or non-terminl in rule RESULT nmes the left-hnd side non-terminl. The Jv clsses of the symols re defined in the terminl nd non-terminl declrtion sections. For exmple, prog ::= LBRACE:l stmts:s RBRACE {: RESULT = new csxlitenode(s, l.linenum,l.colnum) This corresponds to the production prog { stmts } The left rce is nmed l the stmts non-terminl is clled s. In the ction code, new CSXLiteNode is creted nd ssigned to prog. It is constructed from the AST node ssocited with s. Its line nd column numers re those given to the left rce, l (y the scnner). To tell CUP wht non-terminl to use s the strt symol (prog in our exmple), we use the directive: strt with prog

3 Exmple Let s look t the CUP specifiction for CSX-lite. Recll its CFG is progrm { stmts } stmts stmt stmts λ stmt id = expr if ( expr ) stmt expr expr + id expr - id id The corresponding CUP specifiction is: /*** This Is A Jv CUP Specifiction For CSX-lite, Smll Suset of The CSX Lnguge, Used In Cs536 ***/ /* Preliminries to set up nd use the scnner. */ import jv_cup.runtime.* prser code {: pulic void syntx_error (Symol cur_token){ report_error( CSX syntx error t line + String.vlueOf(((CSXToken) cur_token.vlue).linenum), null)} init with {: scn with {: return Scnner.next_token() /* Terminls (tokens returned y the scnner). */ terminl CSXIdentifierToken IDENTIFIER terminl CSXToken SEMI, LPAREN, RPAREN, ASG, LBRACE, RBRACE terminl CSXToken PLUS, MINUS, rw_if /* Non terminls */ non terminl csxlitenode prog non terminl stmtsnode stmts non terminl stmtnode stmt non terminl exprnode exp non terminl ident strt with prog prog::= LBRACE:l stmts:s RBRACE new csxlitenode(s, l.linenum,l.colnum) stmts::= stmt:s1 stmts:s2 new stmtsnode(s1,s2, s1.linenum,s1.colnum) stmtsnode.null stmt::= ident:id ASG exp:e SEMI new sgnode(id,e, id.linenum,id.colnum) rw_if:i LPAREN exp:e RPAREN stmt:s new ifthennode(e,s, stmtnode.null, i.linenum,i.colnum) exp::= exp:leftvl PLUS:op ident:rightvl new inryopnode(leftvl, sym.plus, rightvl, op.linenum,op.colnum) exp:leftvl MINUS:op ident:rightvl new inryopnode(leftvl, sym.minus,rightvl, op.linenum,op.colnum) ident:i {: RESULT = i

4 ident::= IDENTIFIER:i {: RESULT = new ( new (i.identifiertext, i.linenum,i.colnum), exprnode.null, i.linenum,i.colnum) Let s prse { = } First, is prsed using ident::= IDENTIFIER:i {: RESULT = new ( new (i.identifiertext, i.linenum,i.colnum), exprnode.null, i.linenum,i.colnum) We uild Next, is prsed using ident::= IDENTIFIER:i {: RESULT = new ( new (i.identifiertext, i.linenum,i.colnum), exprnode.null, i.linenum,i.colnum) We uild Then s sutree is recognized s n exp: ident:i {: RESULT = i Now the ssignment sttement is recognized: stmt::= ident:id ASG exp:e SEMI new sgnode(id,e, id.linenum,id.colnum) We uild sgnode

5 The stmts λ production is mtched (indicting tht there re no more sttements in the progrm). CUP mtches stmts::= stmtsnode.null nd we uild This uilds stmtsnode sgnode nullstmtsnode nullstmtsnode Next, stmts stmt stmts is mtched using stmts::= stmt:s1 stmts:s2 new stmtsnode(s1,s2, s1.linenum,s1.colnum) As the lst step of the prse, the prser mtches progrm { stmts } using the CUP rule prog::= LBRACE:l stmts:s RBRACE new csxlitenode(s, l.linenum,l.colnum) The finl AST reurned y the prser is csxlitenode stmtsnode sgnode nullstmtsnode Errors in Context-Free Grmmrs Context-free grmmrs cn contin errors, just s progrms do. Some errors re esy to detect nd fix others re more sutle. In context-free grmmrs we strt with the strt symol, nd pply productions until terminl string is produced. Some context-free grmmrs my contin useless non-terminls. Non-terminls tht re unrechle (from the strt symol) or tht derive no terminl string re considered useless. Useless non-terminls (nd productions tht involve them) cn e sfely removed from

6 grmmr without chnging the lnguge defined y the grmmr. A grmmr contining useless non-terminls is sid to e nonreduced. After useless non-terminls re removed, the grmmr is reduced. Consider S A B x B A A C d Which non-terminls re unrechle? Which derive no terminl string? Finding Useless Non-terminls To find non-terminls tht cn derive one or more terminl strings, we ll use mrking lgorithm. We itertively mrk terminls tht cn derive string of terminls, until no more non-terminls cn e mrked. Unmrked nonterminls re useless. (1) Mrk ll terminl symols (2) Repet If ll symols on the righthnd side of production re mrked Then mrk the lefthnd side Until no more non-terminls cn e mrked We cn use similr mrking lgorithm to determine which non-terminls cn e reched from the strt symol: (1) Mrk the Strt Symol (2) Repet If the lefthnd side of production is mrked Then mrk ll non-terminls in the righthnd side Until no more non-terminls cn e mrked 242

Homework 3 Solutions

Homework 3 Solutions CS 341: Foundtions of Computer Science II Prof. Mrvin Nkym Homework 3 Solutions 1. Give NFAs with the specified numer of sttes recognizing ech of the following lnguges. In ll cses, the lphet is Σ = {,1}.

More information

Regular Sets and Expressions

Regular Sets and Expressions Regulr Sets nd Expressions Finite utomt re importnt in science, mthemtics, nd engineering. Engineers like them ecuse they re super models for circuits (And, since the dvent of VLSI systems sometimes finite

More information

Protocol Analysis. 17-654/17-764 Analysis of Software Artifacts Kevin Bierhoff

Protocol Analysis. 17-654/17-764 Analysis of Software Artifacts Kevin Bierhoff Protocol Anlysis 17-654/17-764 Anlysis of Softwre Artifcts Kevin Bierhoff Tke-Awys Protocols define temporl ordering of events Cn often be cptured with stte mchines Protocol nlysis needs to py ttention

More information

A Visual and Interactive Input abb Automata. Theory Course with JFLAP 4.0

A Visual and Interactive Input abb Automata. Theory Course with JFLAP 4.0 Strt Puse Step Noninverted Tree A Visul nd Interctive Input Automt String ccepted! 5 nodes generted. Theory Course with JFLAP 4.0 q0 even 's, even 's q2 even 's, odd 's q1 odd 's, even 's q3 odd 's, odd

More information

Modular Generic Verification of LTL Properties for Aspects

Modular Generic Verification of LTL Properties for Aspects Modulr Generic Verifiction of LTL Properties for Aspects Mx Goldmn Shmuel Ktz Computer Science Deprtment Technion Isrel Institute of Technology {mgoldmn, ktz}@cs.technion.c.il ABSTRACT Aspects re seprte

More information

Section 5-4 Trigonometric Functions

Section 5-4 Trigonometric Functions 5- Trigonometric Functions Section 5- Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form

More information

AntiSpyware Enterprise Module 8.5

AntiSpyware Enterprise Module 8.5 AntiSpywre Enterprise Module 8.5 Product Guide Aout the AntiSpywre Enterprise Module The McAfee AntiSpywre Enterprise Module 8.5 is n dd-on to the VirusScn Enterprise 8.5i product tht extends its ility

More information

flex Regular Expressions and Lexical Scanning Regular Expressions and flex Examples on Alphabet A = {a,b} (Standard) Regular Expressions on Alphabet A

flex Regular Expressions and Lexical Scanning Regular Expressions and flex Examples on Alphabet A = {a,b} (Standard) Regular Expressions on Alphabet A flex Regulr Expressions nd Lexicl Scnning Using flex to Build Scnner flex genertes lexicl scnners: progrms tht discover tokens. Tokens re the smllest meningful units of progrm (or other string). flex is

More information

One Minute To Learn Programming: Finite Automata

One Minute To Learn Programming: Finite Automata Gret Theoreticl Ides In Computer Science Steven Rudich CS 15-251 Spring 2005 Lecture 9 Fe 8 2005 Crnegie Mellon University One Minute To Lern Progrmming: Finite Automt Let me tech you progrmming lnguge

More information

1.00/1.001 Introduction to Computers and Engineering Problem Solving Fall 2011 - Final Exam

1.00/1.001 Introduction to Computers and Engineering Problem Solving Fall 2011 - Final Exam 1./1.1 Introduction to Computers nd Engineering Problem Solving Fll 211 - Finl Exm Nme: MIT Emil: TA: Section: You hve 3 hours to complete this exm. In ll questions, you should ssume tht ll necessry pckges

More information

Concept Formation Using Graph Grammars

Concept Formation Using Graph Grammars Concept Formtion Using Grph Grmmrs Istvn Jonyer, Lwrence B. Holder nd Dine J. Cook Deprtment of Computer Science nd Engineering University of Texs t Arlington Box 19015 (416 Ytes St.), Arlington, TX 76019-0015

More information

Solutions for Selected Exercises from Introduction to Compiler Design

Solutions for Selected Exercises from Introduction to Compiler Design Solutions for Selected Exercises from Introduction to Compiler Design Torben Æ. Mogensen Lst updte: My 30, 2011 1 Introduction This document provides solutions for selected exercises from Introduction

More information

Reasoning to Solve Equations and Inequalities

Reasoning to Solve Equations and Inequalities Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing

More information

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( ) Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +

More information

Algebra Review. How well do you remember your algebra?

Algebra Review. How well do you remember your algebra? Algebr Review How well do you remember your lgebr? 1 The Order of Opertions Wht do we men when we write + 4? If we multiply we get 6 nd dding 4 gives 10. But, if we dd + 4 = 7 first, then multiply by then

More information

On decidability of LTL model checking for process rewrite systems

On decidability of LTL model checking for process rewrite systems Act Informtic (2009) 46:1 28 DOI 10.1007/s00236-008-0082-3 ORIGINAL ARTICLE On decidbility of LTL model checking for process rewrite systems Lur Bozzelli Mojmír Křetínský Vojtěch Řehák Jn Strejček Received:

More information

Integration by Substitution

Integration by Substitution Integrtion by Substitution Dr. Philippe B. Lvl Kennesw Stte University August, 8 Abstrct This hndout contins mteril on very importnt integrtion method clled integrtion by substitution. Substitution is

More information

Object Semantics. 6.170 Lecture 2

Object Semantics. 6.170 Lecture 2 Object Semntics 6.170 Lecture 2 The objectives of this lecture re to: to help you become fmilir with the bsic runtime mechnism common to ll object-oriented lnguges (but with prticulr focus on Jv): vribles,

More information

0.1 Basic Set Theory and Interval Notation

0.1 Basic Set Theory and Interval Notation 0.1 Bsic Set Theory nd Intervl Nottion 3 0.1 Bsic Set Theory nd Intervl Nottion 0.1.1 Some Bsic Set Theory Notions Like ll good Mth ooks, we egin with definition. Definition 0.1. A set is well-defined

More information

FORMAL LANGUAGES, AUTOMATA AND THEORY OF COMPUTATION EXERCISES ON REGULAR LANGUAGES

FORMAL LANGUAGES, AUTOMATA AND THEORY OF COMPUTATION EXERCISES ON REGULAR LANGUAGES FORMAL LANGUAGES, AUTOMATA AND THEORY OF COMPUTATION EXERCISES ON REGULAR LANGUAGES Introduction This compendium contins exercises out regulr lnguges for the course Forml Lnguges, Automt nd Theory of Computtion

More information

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100 hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by

More information

Lecture 3 Gaussian Probability Distribution

Lecture 3 Gaussian Probability Distribution Lecture 3 Gussin Probbility Distribution Introduction l Gussin probbility distribution is perhps the most used distribution in ll of science. u lso clled bell shped curve or norml distribution l Unlike

More information

Virtual Machine. Part II: Program Control. Building a Modern Computer From First Principles. www.nand2tetris.org

Virtual Machine. Part II: Program Control. Building a Modern Computer From First Principles. www.nand2tetris.org Virtul Mchine Prt II: Progrm Control Building Modern Computer From First Principles www.nnd2tetris.org Elements of Computing Systems, Nisn & Schocken, MIT Press, www.nnd2tetris.org, Chpter 8: Virtul Mchine,

More information

Engineer-to-Engineer Note

Engineer-to-Engineer Note Engineer-to-Engineer Note EE-234 Technicl notes on using Anlog Devices DSPs, processors nd development tools Contct our technicl support t dsp.support@nlog.com nd t dsptools.support@nlog.com Or visit our

More information

Helicopter Theme and Variations

Helicopter Theme and Variations Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the

More information

PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY

PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive

More information

Engineer-to-Engineer Note

Engineer-to-Engineer Note Engineer-to-Engineer Note EE-280 Technicl notes on using Anlog Devices DSPs, processors nd development tools Visit our Web resources http://www.nlog.com/ee-notes nd http://www.nlog.com/processors or e-mil

More information

Bypassing Space Explosion in Regular Expression Matching for Network Intrusion Detection and Prevention Systems

Bypassing Space Explosion in Regular Expression Matching for Network Intrusion Detection and Prevention Systems Bypssing Spce Explosion in Regulr Expression Mtching for Network Intrusion Detection n Prevention Systems Jignesh Ptel, Alex Liu n Eric Torng Dept. of Computer Science n Engineering Michign Stte University

More information

Generating In-Line Monitors For Rabin Automata

Generating In-Line Monitors For Rabin Automata Generting In-Line Monitors For Rin Automt Hugues Chot, Rphel Khoury, nd Ndi Twi Lvl University, Deprtment of Computer Science nd Softwre Engineering, Pvillon Adrien-Pouliot, 1065, venue de l Medecine Queec

More information

IaaS Configuration for Virtual Platforms

IaaS Configuration for Virtual Platforms IS Configurtion for Virtul Pltforms vcloud Automtion Center 6.0 This document supports the version of ech product listed nd supports ll susequent versions until the document is replced y new edition. To

More information

Network Configuration Independence Mechanism

Network Configuration Independence Mechanism 3GPP TSG SA WG3 Security S3#19 S3-010323 3-6 July, 2001 Newbury, UK Source: Title: Document for: AT&T Wireless Network Configurtion Independence Mechnism Approvl 1 Introduction During the lst S3 meeting

More information

Hillsborough Township Public Schools Mathematics Department Computer Programming 1

Hillsborough Township Public Schools Mathematics Department Computer Programming 1 Essentil Unit 1 Introduction to Progrmming Pcing: 15 dys Common Unit Test Wht re the ethicl implictions for ming in tody s world? There re ethicl responsibilities to consider when writing computer s. Citizenship,

More information

Scanning and parsing. Topics. Announcements Pick a partner by Monday Makeup lecture will be on Monday August 29th at 3pm

Scanning and parsing. Topics. Announcements Pick a partner by Monday Makeup lecture will be on Monday August 29th at 3pm Scanning and Parsing Announcements Pick a partner by Monday Makeup lecture will be on Monday August 29th at 3pm Today Outline of planned topics for course Overall structure of a compiler Lexical analysis

More information

Engineer-to-Engineer Note

Engineer-to-Engineer Note Engineer-to-Engineer Note EE-265 Technicl notes on using Anlog Devices DSPs, processors nd development tools Contct our technicl support t dsp.support@nlog.com nd t dsptools.support@nlog.com Or visit our

More information

Pentominoes. Pentominoes. Bruce Baguley Cascade Math Systems, LLC. The pentominoes are a simple-looking set of objects through which some powerful

Pentominoes. Pentominoes. Bruce Baguley Cascade Math Systems, LLC. The pentominoes are a simple-looking set of objects through which some powerful Pentominoes Bruce Bguley Cscde Mth Systems, LLC Astrct. Pentominoes nd their reltives the polyominoes, polycues, nd polyhypercues will e used to explore nd pply vrious importnt mthemticl concepts. In this

More information

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered: Appendi D: Completing the Squre nd the Qudrtic Formul Fctoring qudrtic epressions such s: + 6 + 8 ws one of the topics introduced in Appendi C. Fctoring qudrtic epressions is useful skill tht cn help you

More information

5 a LAN 6 a gateway 7 a modem

5 a LAN 6 a gateway 7 a modem STARTER With the help of this digrm, try to descrie the function of these components of typicl network system: 1 file server 2 ridge 3 router 4 ckone 5 LAN 6 gtewy 7 modem Another Novell LAN Router Internet

More information

STRM Log Manager Installation Guide

STRM Log Manager Installation Guide Security Thret Response Mnger Relese 2012.0 Juniper Networks, Inc. 1194 North Mthild Avenue Sunnyvle, CA 94089 USA 408-745-2000 www.juniper.net Pulished: 2012-09-12 Copyright Notice Copyright 2012 Juniper

More information

9 CONTINUOUS DISTRIBUTIONS

9 CONTINUOUS DISTRIBUTIONS 9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete

More information

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions. Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd

More information

Gene Expression Programming: A New Adaptive Algorithm for Solving Problems

Gene Expression Programming: A New Adaptive Algorithm for Solving Problems Gene Expression Progrmming: A New Adptive Algorithm for Solving Prolems Cândid Ferreir Deprtmento de Ciêncis Agráris Universidde dos Açores 9701-851 Terr-Chã Angr do Heroísmo, Portugl Complex Systems,

More information

Automated Grading of DFA Constructions

Automated Grading of DFA Constructions Automted Grding of DFA Constructions Rjeev Alur nd Loris D Antoni Sumit Gulwni Dileep Kini nd Mhesh Viswnthn Deprtment of Computer Science Microsoft Reserch Deprtment of Computer Science University of

More information

trademark and symbol guidelines FOR CORPORATE STATIONARY APPLICATIONS reviewed 01.02.2007

trademark and symbol guidelines FOR CORPORATE STATIONARY APPLICATIONS reviewed 01.02.2007 trdemrk nd symbol guidelines trdemrk guidelines The trdemrk Cn be plced in either of the two usul configurtions but horizontl usge is preferble. Wherever possible the trdemrk should be plced on blck bckground.

More information

Regular Languages and Finite Automata

Regular Languages and Finite Automata N Lecture Notes on Regulr Lnguges nd Finite Automt for Prt IA of the Computer Science Tripos Mrcelo Fiore Cmbridge University Computer Lbortory First Edition 1998. Revised 1999, 2000, 2001, 2002, 2003,

More information

CS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001

CS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001 CS99S Lortory 2 Preprtion Copyright W. J. Dlly 2 Octoer, 2 Ojectives:. Understnd the principle of sttic CMOS gte circuits 2. Build simple logic gtes from MOS trnsistors 3. Evlute these gtes to oserve logic

More information

Lecture 5. Inner Product

Lecture 5. Inner Product Lecture 5 Inner Product Let us strt with the following problem. Given point P R nd line L R, how cn we find the point on the line closest to P? Answer: Drw line segment from P meeting the line in right

More information

Math 135 Circles and Completing the Square Examples

Math 135 Circles and Completing the Square Examples Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for

More information

Regular Repair of Specifications

Regular Repair of Specifications Regulr Repir of Specifictions Michel Benedikt Oxford University michel.enedikt@coml.ox.c.uk Griele Puppis Oxford University griele.puppis@coml.ox.c.uk Cristin Riveros Oxford University cristin.riveros@coml.ox.c.uk

More information

Words Symbols Diagram. abcde. a + b + c + d + e

Words Symbols Diagram. abcde. a + b + c + d + e Logi Gtes nd Properties We will e using logil opertions to uild mhines tht n do rithmeti lultions. It s useful to think of these opertions s si omponents tht n e hooked together into omplex networks. To

More information

Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.

Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3. The nlysis of vrince (ANOVA) Although the t-test is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the t-test cn be used to compre the mens of only

More information

LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES

LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES DAVID WEBB CONTENTS Liner trnsformtions 2 The representing mtrix of liner trnsformtion 3 3 An ppliction: reflections in the plne 6 4 The lgebr of

More information

Pre-Approval Application

Pre-Approval Application Pre-Approvl Appliction In tody s rel estte mrket, Pre-Approved mortgge provides you the buyer with powerful tool in the home purchse process! Once you hve received your Pre-Approvl, you cn shop for your

More information

Lec 2: Gates and Logic

Lec 2: Gates and Logic Lec 2: Gtes nd Logic Kvit Bl CS 34, Fll 28 Computer Science Cornell University Announcements Clss newsgroup creted Posted on we-pge Use it for prtner finding First ssignment is to find prtners Due this

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

Example 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.

Example 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers. 2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this

More information

How fast can we sort? Sorting. Decision-tree model. Decision-tree for insertion sort Sort a 1, a 2, a 3. CS 3343 -- Spring 2009

How fast can we sort? Sorting. Decision-tree model. Decision-tree for insertion sort Sort a 1, a 2, a 3. CS 3343 -- Spring 2009 CS 4 -- Spring 2009 Sorting Crol Wenk Slides courtesy of Chrles Leiserson with smll chnges by Crol Wenk CS 4 Anlysis of Algorithms 1 How fst cn we sort? All the sorting lgorithms we hve seen so fr re comprison

More information

Lifestyles. 1 Warm-up. 2 Conversation. Talk about the pictures with a partner. Who are these people? Where are they? Listen and read.

Lifestyles. 1 Warm-up. 2 Conversation. Talk about the pictures with a partner. Who are these people? Where are they? Listen and read. 6 Lifestyles Focus Grmmr lifestyles Vocbulry common verbs djectives simple present I/you/we/they Yes/No questions 1 Wrm-up Tlk bout the pictures with prtner. Who re these people? Where re they? 2 Converstion

More information

Rotational Equilibrium: A Question of Balance

Rotational Equilibrium: A Question of Balance Prt of the IEEE Techer In-Service Progrm - Lesson Focus Demonstrte the concept of rottionl equilirium. Lesson Synopsis The Rottionl Equilirium ctivity encourges students to explore the sic concepts of

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

Outline of the Lecture. Software Testing. Unit & Integration Testing. Components. Lecture Notes 3 (of 4)

Outline of the Lecture. Software Testing. Unit & Integration Testing. Components. Lecture Notes 3 (of 4) Outline of the Lecture Softwre Testing Lecture Notes 3 (of 4) Integrtion Testing Top-down ottom-up ig-ng Sndwich System Testing cceptnce Testing istriution of ults in lrge Industril Softwre System (ISST

More information

How To Network A Smll Business

How To Network A Smll Business Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

EQUATIONS OF LINES AND PLANES

EQUATIONS OF LINES AND PLANES EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in point-direction nd twopoint

More information

Vector differentiation. Chapters 6, 7

Vector differentiation. Chapters 6, 7 Chpter 2 Vectors Courtesy NASA/JPL-Cltech Summry (see exmples in Hw 1, 2, 3) Circ 1900 A.D., J. Willird Gis invented useful comintion of mgnitude nd direction clled vectors nd their higher-dimensionl counterprts

More information

Factoring Polynomials

Factoring Polynomials Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles

More information

Firm Objectives. The Theory of the Firm II. Cost Minimization Mathematical Approach. First order conditions. Cost Minimization Graphical Approach

Firm Objectives. The Theory of the Firm II. Cost Minimization Mathematical Approach. First order conditions. Cost Minimization Graphical Approach Pro. Jy Bhttchry Spring 200 The Theory o the Firm II st lecture we covered: production unctions Tody: Cost minimiztion Firm s supply under cost minimiztion Short vs. long run cost curves Firm Ojectives

More information

DATABASDESIGN FÖR INGENJÖRER - 1056F

DATABASDESIGN FÖR INGENJÖRER - 1056F DATABASDESIGN FÖR INGENJÖRER - 06F Sommr 00 En introuktionskurs i tssystem http://user.it.uu.se/~ul/t-sommr0/ lt. http://www.it.uu.se/eu/course/homepge/esign/st0/ Kjell Orsorn (Rusln Fomkin) Uppsl Dtse

More information

Vectors 2. 1. Recap of vectors

Vectors 2. 1. Recap of vectors Vectors 2. Recp of vectors Vectors re directed line segments - they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms

More information

The Semantics of Graph Programs

The Semantics of Graph Programs The Semntics of Grph Progrms Detlef Plump Deprtment of Computer Science The University of York, UK Sndr Steinert Deprtment of Computer Science The University of York, UK GP (for Grph Progrms) is rule-bsed,

More information

Or more simply put, when adding or subtracting quantities, their uncertainties add.

Or more simply put, when adding or subtracting quantities, their uncertainties add. Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re

More information

1.2 The Integers and Rational Numbers

1.2 The Integers and Rational Numbers .2. THE INTEGERS AND RATIONAL NUMBERS.2 The Integers n Rtionl Numers The elements of the set of integers: consist of three types of numers: Z {..., 5, 4, 3, 2,, 0,, 2, 3, 4, 5,...} I. The (positive) nturl

More information

Answer, Key Homework 10 David McIntyre 1

Answer, Key Homework 10 David McIntyre 1 Answer, Key Homework 10 Dvid McIntyre 1 This print-out should hve 22 questions, check tht it is complete. Multiple-choice questions my continue on the next column or pge: find ll choices efore mking your

More information

Enterprise Risk Management Software Buyer s Guide

Enterprise Risk Management Software Buyer s Guide Enterprise Risk Mngement Softwre Buyer s Guide 1. Wht is Enterprise Risk Mngement? 2. Gols of n ERM Progrm 3. Why Implement ERM 4. Steps to Implementing Successful ERM Progrm 5. Key Performnce Indictors

More information

Euler Euler Everywhere Using the Euler-Lagrange Equation to Solve Calculus of Variation Problems

Euler Euler Everywhere Using the Euler-Lagrange Equation to Solve Calculus of Variation Problems Euler Euler Everywhere Using the Euler-Lgrnge Eqution to Solve Clculus of Vrition Problems Jenine Smllwood Principles of Anlysis Professor Flschk My 12, 1998 1 1. Introduction Clculus of vritions is brnch

More information

Unit 6: Exponents and Radicals

Unit 6: Exponents and Radicals Eponents nd Rdicls -: The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N): - counting numers. {,,,,, } Whole Numers (W): - counting numers with 0. {0,,,,,, } Integers (I): -

More information

Review guide for the final exam in Math 233

Review guide for the final exam in Math 233 Review guide for the finl exm in Mth 33 1 Bsic mteril. This review includes the reminder of the mteril for mth 33. The finl exm will be cumultive exm with mny of the problems coming from the mteril covered

More information

body.allow-sidebar OR.no-sidebar.home-page (if this is the home page).has-custom-banner OR.nocustom-banner .IR OR.no-IR

body.allow-sidebar OR.no-sidebar.home-page (if this is the home page).has-custom-banner OR.nocustom-banner .IR OR.no-IR body.llow-sidebr OR.no-sidebr.home-pge (if this is the home pge).hs-custom-bnner OR.nocustom-bnner.IR OR.no-IR #IDENTIFIER_FOR_THIS_SITE div#pge-continer.depends_on_page_ty PE llow-sidebr mens tht there

More information

Unambiguous Recognizable Two-dimensional Languages

Unambiguous Recognizable Two-dimensional Languages Unmbiguous Recognizble Two-dimensionl Lnguges Mrcell Anselmo, Dor Gimmrresi, Mri Mdoni, Antonio Restivo (Univ. of Slerno, Univ. Rom Tor Vergt, Univ. of Ctni, Univ. of Plermo) W2DL, My 26 REC fmily I REC

More information

Operations with Polynomials

Operations with Polynomials 38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply

More information

MATH 150 HOMEWORK 4 SOLUTIONS

MATH 150 HOMEWORK 4 SOLUTIONS MATH 150 HOMEWORK 4 SOLUTIONS Section 1.8 Show tht the product of two of the numbers 65 1000 8 2001 + 3 177, 79 1212 9 2399 + 2 2001, nd 24 4493 5 8192 + 7 1777 is nonnegtive. Is your proof constructive

More information

Small Businesses Decisions to Offer Health Insurance to Employees

Small Businesses Decisions to Offer Health Insurance to Employees Smll Businesses Decisions to Offer Helth Insurnce to Employees Ctherine McLughlin nd Adm Swinurn, June 2014 Employer-sponsored helth insurnce (ESI) is the dominnt source of coverge for nonelderly dults

More information

Warm-up for Differential Calculus

Warm-up for Differential Calculus Summer Assignment Wrm-up for Differentil Clculus Who should complete this pcket? Students who hve completed Functions or Honors Functions nd will be tking Differentil Clculus in the fll of 015. Due Dte:

More information

Pointed Regular Expressions

Pointed Regular Expressions Pointed Regulr Expressions Andre Asperti 1, Cludio Scerdoti Coen 1, nd Enrico Tssi 2 1 Deprtment of Computer Science, University of Bologn sperti@cs.unio.it scerdot@cs.unio.it 2 INRIA-Micorsoft tssi@cs.unio.it

More information

VMware Horizon Mirage Web Manager Guide

VMware Horizon Mirage Web Manager Guide VMwre Horizon Mirge We Mnger Guide Horizon Mirge 4.3 This document supports the version of ech product listed nd supports ll susequent versions until the document is replced y new edition. To check for

More information

Tool Support for Feature-Oriented Software Development

Tool Support for Feature-Oriented Software Development Tool Support for Feture-Oriented Softwre Development FetureIDE: An Eclipse-Bsed Approch Thoms Leich leich@iti.cs.unimgdeurg.de Sven Apel pel@iti.cs.unimgdeurg.de Lur Mrnitz mrnitz@cs.unimgdeurg.de ABSTRACT

More information

How To Set Up A Network For Your Business

How To Set Up A Network For Your Business Why Network is n Essentil Productivity Tool for Any Smll Business TechAdvisory.org SME Reports sponsored by Effective technology is essentil for smll businesses looking to increse their productivity. Computer

More information

Your duty, however, does not require disclosure of matter:

Your duty, however, does not require disclosure of matter: Your Duty of Disclosure Before you enter into contrct of generl insurnce with n insurer, you hve duty, under the Insurnce Contrcts Act 1984 (Cth), to disclose to the insurer every mtter tht you know, or

More information

and thus, they are similar. If k = 3 then the Jordan form of both matrices is

and thus, they are similar. If k = 3 then the Jordan form of both matrices is Homework ssignment 11 Section 7. pp. 249-25 Exercise 1. Let N 1 nd N 2 be nilpotent mtrices over the field F. Prove tht N 1 nd N 2 re similr if nd only if they hve the sme miniml polynomil. Solution: If

More information

Vectors and dyadics. Chapter 2. Summary. 2.1 Examples of scalars, vectors, and dyadics

Vectors and dyadics. Chapter 2. Summary. 2.1 Examples of scalars, vectors, and dyadics Chpter 2 Vectors nd dydics Summry Circ 1900 A.D., J. Willird Gis proposed the ide of vectors nd their higher-dimensionl counterprts dydics, tridics, ndpolydics. Vectors descrie three-dimensionl spce nd

More information

Basic Research in Computer Science BRICS RS-02-13 Brodal et al.: Solving the String Statistics Problem in Time O(n log n)

Basic Research in Computer Science BRICS RS-02-13 Brodal et al.: Solving the String Statistics Problem in Time O(n log n) BRICS Bsic Reserch in Computer Science BRICS RS-02-13 Brodl et l.: Solving the String Sttistics Prolem in Time O(n log n) Solving the String Sttistics Prolem in Time O(n log n) Gerth Stølting Brodl Rune

More information

Graphs on Logarithmic and Semilogarithmic Paper

Graphs on Logarithmic and Semilogarithmic Paper 0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl

More information

Vectors and dyadics. Chapter 2. Summary. 2.1 Examples of scalars, vectors, and dyadics

Vectors and dyadics. Chapter 2. Summary. 2.1 Examples of scalars, vectors, and dyadics Chpter 2 Vectors nd dydics Summry Circ 1900 A.D., J. Willird Gis proposed the ide of vectors nd their higher-dimensionl counterprts dydics, tridics, ndpolydics. Vectors descrie three-dimensionl spce nd

More information

FAULT TREES AND RELIABILITY BLOCK DIAGRAMS. Harry G. Kwatny. Department of Mechanical Engineering & Mechanics Drexel University

FAULT TREES AND RELIABILITY BLOCK DIAGRAMS. Harry G. Kwatny. Department of Mechanical Engineering & Mechanics Drexel University SYSTEM FAULT AND Hrry G. Kwtny Deprtment of Mechnicl Engineering & Mechnics Drexel University OUTLINE SYSTEM RBD Definition RBDs nd Fult Trees System Structure Structure Functions Pths nd Cutsets Reliility

More information

1. In the Bohr model, compare the magnitudes of the electron s kinetic and potential energies in orbit. What does this imply?

1. In the Bohr model, compare the magnitudes of the electron s kinetic and potential energies in orbit. What does this imply? Assignment 3: Bohr s model nd lser fundmentls 1. In the Bohr model, compre the mgnitudes of the electron s kinetic nd potentil energies in orit. Wht does this imply? When n electron moves in n orit, the

More information

Complexity Results in Epistemic Planning

Complexity Results in Epistemic Planning Proceedings of the Twenty-Fourth Interntionl Joint Conference on Artificil Intelligence (IJCAI 2015) Complexity Results in Epistemic Plnning Thoms Bolnder DTU Compute Tech. University of Denmrk Copenhgen,

More information

2 DIODE CLIPPING and CLAMPING CIRCUITS

2 DIODE CLIPPING and CLAMPING CIRCUITS 2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of

More information

Babylonian Method of Computing the Square Root: Justifications Based on Fuzzy Techniques and on Computational Complexity

Babylonian Method of Computing the Square Root: Justifications Based on Fuzzy Techniques and on Computational Complexity Bbylonin Method of Computing the Squre Root: Justifictions Bsed on Fuzzy Techniques nd on Computtionl Complexity Olg Koshelev Deprtment of Mthemtics Eduction University of Texs t El Pso 500 W. University

More information

Quick Guide to Lisp Implementation

Quick Guide to Lisp Implementation isp Implementtion Hndout Pge 1 o 10 Quik Guide to isp Implementtion Representtion o si dt strutures isp dt strutures re lled S-epressions. The representtion o n S-epression n e roken into two piees, the

More information