Book ChapterDOI
Reachability Analysis of Pushdown Automata: Application to Model-Checking
Ahmed Bouajjani,Javier Esparza,Oded Maler +2 more
- pp 135-150
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TLDR
This work considers the more general class of alternating pushdown systems and uses alternating finite-state automata as a representation structure for sets of their configurations and gives a simple and natural procedure to compute sets of predecessors using this representation structure.Abstract:
We apply the symbolic analysis principle to pushdown systems. We represent (possibly infinite) sets of configurations of such systems by means of finite-state automata. In order to reason in a uniform way about analysis problems involving both existential and universal path quantification (such as model-checking for branching-time logics), we consider the more general class of alternating pushdown systems and use alternating finite-state automata as a representation structure for sets of their configurations. We give a simple and natural procedure to compute sets of predecessors using this representation structure. We incorporate this procedure into the automata-theoretic approach to model-checking to define new model-checking algorithms for pushdown systems against both linear and branching-time properties. From these results we derive upper bounds for several model-checking problems as well as matching lower bounds.read more
Citations
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Book ChapterDOI
A Temporal Logic of Nested Calls and Returns
TL;DR: This work introduces a temporal logic of calls and returns (CaRet) for specification and algorithmic verification of correctness requirements of structured programs and presents a tableau construction that reduces the model checking problem to the emptiness problem for a Buchi pushdown system.
Book ChapterDOI
Analysis of Recursive Game Graphs Using Data Flow Equations
TL;DR: In this paper, a finite-state abstraction of a sequential program with potentially recursive procedures and input from the environment is checked statically whether there are input sequences that can drive the system into "bad/good" executions.
Journal Article
Analysis of recursive game graphs using data flow equations
TL;DR: Given a finite-state abstraction of a sequential program with potentially recursive procedures and input from the environment, whether there are input sequences that can drive the system into “bad/good” executions is checked.
Journal ArticleDOI
Recursive Markov chains, stochastic grammars, and monotone systems of nonlinear equations
TL;DR: It is shown that the PSPACE upper bounds cannot be substantially improved without a breakthrough on long standing open problems: the square-root sum problem and an arithmetic circuit decision problem that captures P-time on the unit-cost rational arithmetic RAM model.
Proceedings ArticleDOI
Visibly pushdown languages
Rajeev Alur,P. Madhusudan +1 more
TL;DR: This framework explains, unifies, and generalizes many of the decision procedures in the program analysis literature, and allows algorithmic verification of recursive programs with respect to many context-free properties including access control properties via stack inspection and correctness of procedures withrespect to pre and post conditions.
References
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Journal ArticleDOI
The algorithmic analysis of hybrid systems
Rajeev Alur,Costas Courcoubetis,Nicolas Halbwachs,Thomas A. Henzinger,Pei Ho,Xavier Nicollin,Alfredo Olivero,Joseph Sifakis,Sergio Yovine +8 more
TL;DR: A general framework for the formal specification and algorithmic analysis of hybrid systems is presented, which considers symbolic model-checking and minimization procedures that are based on the reachability analysis of an infinite state space.
An Automata-Theoretic Approach to Automatic Program Verification
Moshe Y. Vardi,Pierre Wolper +1 more
Symbolic model checking: an approach to the state explosion problem
TL;DR: The symbolic model checking technique revealed subtle errors in this protocol, resulting from complex execution sequences that would occur with very low probability in random simulation runs, and an alternative method is developed for avoiding the state explosion in the case of asynchronous control circuits.
Book
String-rewriting systems
Ronald V. Book,Friedrich Otto +1 more
TL;DR: This chapter provides formal definitions of string-rewriting systems and their induced reduction relations and Thue congruences and relies on Section 1.4 for basic definitions and notation for strings.
Proceedings ArticleDOI
Automatic verification of finite state concurrent system using temporal logic specifications: a practical approach
TL;DR: It is argued that this technique can provide a practical alternative to manual proof construction or use of a mechanical theorem prover for verifying many finite state concurrent systems.