Equational approximations for tree automata completion

In this paper we deal with the verification of safety properties of infinite-state systems modeled by term rewriting systems. An over-approximation of the set of reachable terms of a term rewriting system R is obtained by automatically constructing a finite tree automaton. The construction is parameterized by a set E of equations on terms, and we also show that the approximating automata recognize at most the set of R/E-reachable terms. Finally, we present some experiments carried out with the implementation of our algorithm. In particular, we show how some approximations from the literature can be defined using equational approximations.

[1]  Ahmed Bouajjani,et al.  Abstract regular (tree) model checking , 2012, International Journal on Software Tools for Technology Transfer.

[2]  Sophie Tison,et al.  Regular Tree Languages and Rewrite Systems , 1995, Fundam. Informaticae.

[3]  Benoît Boyer,et al.  Certifying a Tree Automata Completion Checker , 2008, IJCAR.

[4]  Ahmed Bouajjani,et al.  Abstract Regular Tree Model Checking of Complex Dynamic Data Structures , 2006, SAS.

[5]  Valérie Viet Triem Tong,et al.  Reachability Analysis over Term Rewriting Systems , 2004, Journal of Automated Reasoning.

[6]  José Meseguer,et al.  Equational abstractions , 2008, Theor. Comput. Sci..

[7]  T. Genet.  Timbuk - A Tree Automata Library , 2003 .

[8]  Tayssir Touili,et al.  Extrapolating Tree Transformations , 2002, CAV.

[9]  Florent Jacquemard,et al.  Decidable Approximations of Term Rewriting Systems , 1996, RTA.

[10]  David Sinclair,et al.  Automatic Approximation for the Verification of Cryptographic Protocols , 2002, FASec.

[11]  Valérie Viet Triem Tong,et al.  Reachability Analysis of Term Rewriting Systems with Timbuk , 2001, LPAR.

[12]  Yohan Boichut,et al.  Rewriting Approximations for Fast Prototyping of Static Analyzers , 2007, RTA.

[13]  Parosh Aziz Abdulla,et al.  Tree regular model checking: A simulation-based approach , 2006, J. Log. Algebraic Methods Program..

[14]  Michaël Rusinowitch,et al.  Closure of Hedge-Automata Languages by Hedge Rewriting , 2008, RTA.

[15]  Thomas Genet,et al.  Rewriting for Cryptographic Protocol Verification , 2000, CADE.

[16]  John P. Gallagher,et al.  Approximating Term Rewriting Systems: A Horn Clause Specification and Its Implementation , 2008, LPAR.

[17]  Tobias Nipkow,et al.  Term rewriting and all that , 1998 .

[18]  Thomas Genet,et al.  Decidable Approximations of Sets of Descendants and Sets of Normal Forms , 1998, RTA.

[19]  Anca Muscholl,et al.  Tree Pattern Rewriting Systems , 2008, ATVA.

[20]  J. Van Leeuwen,et al.  Handbook of theoretical computer science - Part A: Algorithms and complexity; Part B: Formal models and semantics , 1990 .

[21]  Toshinori Takai,et al.  A Verification Technique Using Term Rewriting Systems and Abstract Interpretation , 2004, RTA.

[22]  Pierre-Etienne Moreau,et al.  Towards an Efficient Implementation of Tree Automata Completion , 2008, AMAST.

[23]  Jean-Pierre Jouannaud,et al.  Rewrite Systems , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[24]  Valérie Viet Triem Tong,et al.  Proving Negative Conjectures on Equational Theories using Induction and Abstract Interpretation , 2002 .

[25]  Joxan Jaffar,et al.  A finite presentation theorem for approximating logic programs , 1989, POPL '90.

[26]  Neil D. Jones,et al.  Flow analysis of lazy higher-order functional programs , 2007, Theor. Comput. Sci..

[27]  Tayssir Touili,et al.  Regular Hedge Model Checking , 2006, IFIP TCS.

[28]  John C. Reynolds,et al.  Automatic computation of data set definitions , 1968, IFIP Congress.

[29]  Tayssir Touili,et al.  On Computing Reachability Sets of Process Rewrite Systems , 2005, RTA.

[30]  Narciso Martí-Oliet,et al.  All About Maude - A High-Performance Logical Framework, How to Specify, Program and Verify Systems in Rewriting Logic , 2007, All About Maude.

[31]  Thomas Genet,et al.  Verification of Copy-Protection Cryptographic Protocol using Approximations of Term Rewriting System , 2003 .

[32]  Hubert Comon,et al.  Tree automata techniques and applications , 1997 .

[33]  Benoît Boyer,et al.  Verifying Temporal Regular Properties of Abstractions of Term Rewriting Systems , 2010, RULE.