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86
Reachability Analysis of Pushdown Automata: Application to ModelChecking
, 1997
"... We apply the symbolic analysis principle to pushdown systems. We represent (possibly infinite) sets of configurations of such systems by means of finitestate automata. In order to reason in a uniform way about analysis problems involving both existential and universal path quantification (like mode ..."
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Cited by 373 (38 self)
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We apply the symbolic analysis principle to pushdown systems. We represent (possibly infinite) sets of configurations of such systems by means of finitestate automata. In order to reason in a uniform way about analysis problems involving both existential and universal path quantification (like modelchecking for branchingtime logics), we consider the more general class of alternating pushdown systems and use alternating finitestate automata as a representation structure for their sets of configurations. We give a simple and natural procedure to compute sets of predecessors for this representation structure. We apply this procedure and the automatatheoretic approach to modelchecking to define new modelchecking algorithms for pushdown systems and both linear and branchingtime properties. From these results we derive upper bounds for several modelchecking problems, and we also provide matching lower bounds, using reductions based on some techniques introduced by Walukiewicz.
Bebop: A Symbolic Model Checker for Boolean Programs
, 2000
"... We present the design, implementation and empirical evaluation of Bebop  a symbolic model checker for boolean programs. Bebop represents control flow explicitly, and sets of states implicitly using BDDs. By harnessing the inherent modularity in procedural abstraction and exploiting the locality of ..."
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Cited by 254 (24 self)
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We present the design, implementation and empirical evaluation of Bebop  a symbolic model checker for boolean programs. Bebop represents control flow explicitly, and sets of states implicitly using BDDs. By harnessing the inherent modularity in procedural abstraction and exploiting the locality of variable scoping, Bebop is able to model check boolean programs with several thousand lines of code, hundreds of procedures, and several thousand variables in a few minutes.
Boolean and Cartesian Abstraction for Model Checking C Programs
, 2001
"... The problem of model checking a specification in form of a C program with recursive procedures and many thousands of lines of code has not been addressed before. In this paper, we show how we attack this problem using an abstraction that is formalized with the Cartesian abstraction. It is implemente ..."
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Cited by 193 (12 self)
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The problem of model checking a specification in form of a C program with recursive procedures and many thousands of lines of code has not been addressed before. In this paper, we show how we attack this problem using an abstraction that is formalized with the Cartesian abstraction. It is implemented through a sourcetosource transformation into a `Boolean' C program; we give an algorithm to compute the transformation with a cost that is exponential in its theoretical worstcase complexity but feasible in practice.
Visibly pushdown languages
, 2004
"... Abstract. We study congruences on words in order to characterize the class of visibly pushdown languages (Vpl), a subclass of contextfree languages. For any language L, we define a natural congruence on words that resembles the syntactic congruence for regular languages, such that this congruence i ..."
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Cited by 183 (19 self)
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Abstract. We study congruences on words in order to characterize the class of visibly pushdown languages (Vpl), a subclass of contextfree languages. For any language L, we define a natural congruence on words that resembles the syntactic congruence for regular languages, such that this congruence is of finite index if, and only if, L is a Vpl. We then study the problem of finding canonical minimal deterministic automata for Vpls. Though Vpls in general do not have unique minimal automata, we consider a subclass of VPAs called kmodule singleentry VPAs that correspond to programs with recursive procedures without input parameters, and show that the class of wellmatched Vpls do indeed have unique minimal kmodule singleentry automata. We also give a polynomial time algorithm that minimizes such kmodule singleentry VPAs. 1 Introduction The class of visibly pushdown languages (Vpl), introduced in [1], is a subclassof contextfree languages accepted by pushdown automata in which the input letter determines the type of operation permitted on the stack. Visibly pushdown languages are closed under all boolean operations, and problems such as inclusion, that are undecidable for contextfree languages, are decidable for Vpl. Vpls are relevant to several applications that use contextfree languages suchas the modelchecking of software programs using their pushdown models [13]. Recent work has shown applications in other contexts: in modeling semanticsof effects in processing XML streams [4], in game semantics for programming languages [5], and in identifying larger classes of pushdown specifications thatadmit decidable problems for infinite games on pushdown graphs [6].
Pushdown Processes: Games and Model Checking
, 1996
"... Games given by transition graphs of pushdown processes are considered. It is shown that ..."
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Cited by 182 (7 self)
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Games given by transition graphs of pushdown processes are considered. It is shown that
Analysis of Recursive State Machines
 In Proceedings of CAV 2001
, 2001
"... . Recursive state machines (RSMs) enhance the power of ordinary state machines by allowing vertices to correspond either to ordinary states or to potentially recursive invocations of other state machines. RSMs can model the control flow in sequential imperative programs containing recursive proc ..."
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Cited by 138 (29 self)
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. Recursive state machines (RSMs) enhance the power of ordinary state machines by allowing vertices to correspond either to ordinary states or to potentially recursive invocations of other state machines. RSMs can model the control flow in sequential imperative programs containing recursive procedure calls. They can be viewed as a visual notation extending Statechartslike hierarchical state machines, where concurrency is disallowed but recursion is allowed. They are also related to various models of pushdown systems studied in the verification and program analysis communities. After introducing RSMs, we focus on whether statespace analysis can be performed efficiently for RSMs. We consider the two central problems for algorithmic analysis and model checking, namely, reachability (is a target state reachable from initial states) and cycle detection (is there a reachable cycle containing an accepting state). We show that both these problems can be solved in time O(n` 2 ) and space O(n`), where n is the size of the recursive machine and ` is the maximum, over all component state machines, of the minimum of the number of entries and the number of exits of each component. We also study the precise relationship between RSMs and closely related models. 1
Adding nesting structure to words
 In Developments in Language Theory, LNCS 4036
, 2006
"... We propose the model of nested words for representation of data with both a linear ordering and a hierarchically nested matching of items. Examples of data with such dual linearhierarchical structure include executions of structured programs, annotated linguistic data, and HTML/XML documents. Neste ..."
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Cited by 113 (17 self)
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We propose the model of nested words for representation of data with both a linear ordering and a hierarchically nested matching of items. Examples of data with such dual linearhierarchical structure include executions of structured programs, annotated linguistic data, and HTML/XML documents. Nested words generalize both words and ordered trees, and allow both word and tree operations. We define nested word automata—finitestate acceptors for nested words, and show that the resulting class of regular languages of nested words has all the appealing theoretical properties that the classical regular word languages enjoys: deterministic nested word automata are as expressive as their nondeterministic counterparts; the class is closed under union, intersection, complementation, concatenation, Kleene*, prefixes, and language homomorphisms; membership, emptiness, language inclusion, and language equivalence are all decidable; and definability in monadic second order logic corresponds exactly to finitestate recognizability. We also consider regular languages of infinite nested words and show that the closure properties, MSOcharacterization, and decidability of decision problems carry over. The linear encodings of nested words give the class of visibly pushdown languages of words, and this class lies between balanced languages and deterministic contextfree languages. We argue that for algorithmic verification of structured programs, instead of viewing the program as a contextfree language over words, one should view it as a regular language of nested words (or equivalently, a visibly pushdown language), and this would allow model checking of many properties (such as stack inspection, prepost conditions) that are not expressible in existing specification logics. We also study the relationship between ordered trees and nested words, and the corresponding automata: while the analysis complexity of nested word automata is the same as that of classical tree automata, they combine both bottomup and topdown traversals, and enjoy expressiveness and succinctness benefits over tree automata. 1
Bisimulation Equivalence is Decidable for all ContextFree Processes
 Information and Computation
, 1995
"... Introduction Over the past decade much attention has been devoted to the study of process calculi such as CCS, ACP and CSP [13]. Of particular interest has been the study of the behavioural semantics of these calculi as given by labelled transition graphs. One important question is when processes c ..."
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Cited by 97 (15 self)
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Introduction Over the past decade much attention has been devoted to the study of process calculi such as CCS, ACP and CSP [13]. Of particular interest has been the study of the behavioural semantics of these calculi as given by labelled transition graphs. One important question is when processes can be said to exhibit the same behaviour, and a plethora of behavioural equivalences exists today. Their main rationale has been to capture behavioural aspects that language or trace equivalences do not take into account. The theory of finitestate systems and their equivalences can now be said to be wellestablished. There are many automatic verification tools for their analysis which incorporate equivalence checking. Sound and complete equational theories exist for the various known equivalences, an elegant example is [18]. One may be led to wonder what the results will look like for infinitestate systems. Although language equivalence is decidable
Model checking of hierarchical state machines
 ACM Trans. Program. Lang. Syst
"... Model checking is emerging as a practical tool for detecting logical errors in early stages of system design. We investigate the model checking of sequential hierarchical (nested) systems, i.e., finitestate machines whose states themselves can be other machines. This nesting ability is common in var ..."
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Cited by 90 (11 self)
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Model checking is emerging as a practical tool for detecting logical errors in early stages of system design. We investigate the model checking of sequential hierarchical (nested) systems, i.e., finitestate machines whose states themselves can be other machines. This nesting ability is common in various software design methodologies, and is available in several commercial modeling tools. The straightforward way to analyze a hierarchical machine is to flatten it (thus incurring an exponential blow up) and apply a modelchecking tool on the resulting ordinary FSM. We show that this flattening can be avoided. We develop algorithms for verifying lineartime requirements whose complexity is polynomial in the size of the hierarchical machine. We also address the verification of branching time requirements and provide efficient algorithms and matching lower bounds.
Verification on Infinite Structures
, 2000
"... In this chapter, we present a hierarchy of infinitestate systems based on the primitive operations of sequential and parallel composition; the hierarchy includes a variety of commonlystudied classes of systems such as contextfree and pushdown automata, and Petri net processes. We then examine the ..."
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Cited by 87 (2 self)
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In this chapter, we present a hierarchy of infinitestate systems based on the primitive operations of sequential and parallel composition; the hierarchy includes a variety of commonlystudied classes of systems such as contextfree and pushdown automata, and Petri net processes. We then examine the equivalence and regularity checking problems for these classes, with special emphasis on bisimulation equivalence, stressing the structural techniques which have been devised for solving these problems. Finally, we explore the model checking problem over these classes with respect to various linear and branchingtime temporal logics.