Checking NFA Equivalence with Bisimulations up to Congruence - PowerPoint PPT Presentation

Checking NFA Equivalence with Bisimulations up to Congruence Filippo Bonchi and Damien Pous CNRS, LIP, ENS Lyon POPL, Roma, 25.1.2o13

Language equivalence of finite automata ◮ Useful for model checking: ◮ check that a program refines its specification ◮ compute a sequence A i of automata until A i ∼ A i +1 (cf. abstract regular model checking) ◮ Useful in proof assistants: ◮ decide the equational theory of Kleene algebra ( R ∪ S ) ⋆ = R ⋆ ; ( S ; R ⋆ ) ⋆ (cf. the ATBR and RelationAlgebra Coq libraries) ◮ This work: a new algorithm Filippo Bonchi & Damien Pous 2/26

Outline Deterministic Automata Non-Deterministic Automata Comparison with other algorithms Filippo Bonchi & Damien Pous 3/26

� � Checking language equivalence Deterministic case, first algorithm: a � z a � y x a a � v u a Filippo Bonchi & Damien Pous 4/26

Checking language equivalence Deterministic case, naive algorithm, correctness: ◮ A relation R is a bisimulation if x R y entails ◮ o ( x ) = o ( y ); ◮ for all a , t a ( x ) R t a ( y ). Filippo Bonchi & Damien Pous 5/26

Checking language equivalence Deterministic case, naive algorithm, correctness: ◮ A relation R is a bisimulation if x R y entails ◮ o ( x ) = o ( y ); ◮ for all a , t a ( x ) R t a ( y ). ◮ Theorem: L ( x ) = L ( y ) iff there exists a bisimulation R with x R y Filippo Bonchi & Damien Pous 5/26

Checking language equivalence Deterministic case, naive algorithm, correctness: ◮ A relation R is a bisimulation if x R y entails ◮ o ( x ) = o ( y ); ◮ for all a , t a ( x ) R t a ( y ). ◮ Theorem: L ( x ) = L ( y ) iff there exists a bisimulation R with x R y The previous algorithm attempts to construct a bisimulation Filippo Bonchi & Damien Pous 5/26

� � Checking language equivalence Deterministic case, naive algorithm: quadratic complexity � · � · � · � · · � · � · � · � · · Filippo Bonchi & Damien Pous 6/26

� � Checking language equivalence Deterministic case, naive algorithm: quadratic complexity � · � · � · � · · � · � · � · � · · 1 pairs Filippo Bonchi & Damien Pous 6/26

� � Checking language equivalence One can stop much earlier � · � · � · � · · � · � · � · � · · 21 pairs Filippo Bonchi & Damien Pous 7/26

� � Checking language equivalence One can stop much earlier � · � · � · � · · � · � · � · � · · 21 20 pairs Filippo Bonchi & Damien Pous 7/26

Checking NFA Equivalence with Bisimulations up to Congruence - PowerPoint PPT Presentation

Checking NFA Equivalence with Bisimulations up to Congruence Filippo Bonchi and Damien Pous CNRS, LIP, ENS Lyon POPL, Roma, 25.1.2o13 Language equivalence of finite automata Useful for model checking: check that a program refines its

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Checking NFA Equivalence with Bisimulations up to Congruence - PowerPoint PPT Presentation

Checking NFA Equivalence with Bisimulations up to Congruence Filippo Bonchi and Damien Pous CNRS, LIP, ENS Lyon POPL, Roma, 25.1.2o13 Language equivalence of finite automata Useful for model checking: check that a program refines its

Equivalence checking of prefix-free transducers and deterministic two-tape automata V.A.

Design Verification Sequential Equivalence Checking Virendra Singh Associate Professor

Decision Diagrams &amp; Equivalence Checking --- Introduction to Formal V Instructor : Debdeep

Complexity of Equivalence Checking Problems Zden ek Sawa Department of Computer Science

Reducing search space for trace equivalence checking FOSAD 2013 Lucca Hirschi LSV, ENS Cachan

Equivalence Checking using Grbner Bases Amr Sayed-Ahmed 1 Daniel Groe 1 , 2 Mathias Soeken 3

CS137: Today Electronic Design Automation Sequential Verification DFA equivalence

On CCZ-Equivalence, Extended-Affine Equivalence and Function Twisting Anne Canteaut, L eo

Jason Baumgartner, Hari Mony, Michael Case, Jun Sawada and Karen Yorav IBM Corporation FMCAD

The Fellowship of the Semiring: Concerning Bisimulations for Quantitative Systems Marino Miculan 1

BISIMULATIONS FOR DIFFERENTIAL EQUATIONS http://sysma.imtlucca.it/tools/erode/ MOTIVATION 1 2

On CCZ-Equivalence, Extended-Affine Equivalence and Function Twisting Anne Canteaut, Lo Perrin

Equivalences 1 Equivalence Definition (Equivalence) Two formulas F and G are (semantically)

Todays Expedition TED highlights Equivalence Relations Equivalence Classes and

Coalgebras in Type Theory Equations CoInductive Types Bisimulations Venanzio Capretta

ProNoBis Probability and Nodeterminism, Bisimulations and Security Journ ee des ARCS 01

3. Satisfiability Checking 3.1 SAT-Checking Procedures Verification Technology

Equivalence Relations {( a , b ) | a and b are from the the same state}. Observe that these

Section 4.2: Equivalence Relations What is equality? What is equivalence? Equality is

CS780 Discrete-State Models Instructor: Peter Kemper R 006, phone 221-3462, email:kemper@cs.wm.edu

Hoare Logic and Model Checking Model Checking Lecture 11: Model checking for Computation Tree

7.5 EQUIVALENCE RELATIONS def: An equivalence relation is a binary rela- tion that is reflexive,

Checking &amp; Spot-Checking the Correctness of Priority Queues Matthew Chu &amp; Sampath Kannan

Statistical Statistical Statistical Model Statistical Model Model Checking Model Checking

Decision Diagrams & Equivalence Checking --- Introduction to Formal V Instructor : Debdeep

Checking & Spot-Checking the Correctness of Priority Queues Matthew Chu & Sampath Kannan