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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 385 (39 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.
An AutomataTheoretic Approach to BranchingTime Model Checking
 JOURNAL OF THE ACM
, 1998
"... Translating linear temporal logic formulas to automata has proven to be an effective approach for implementing lineartime modelchecking, and for obtaining many extensions and improvements to this verification method. On the other hand, for branching temporal logic, automatatheoretic techniques ..."
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Cited by 360 (67 self)
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Translating linear temporal logic formulas to automata has proven to be an effective approach for implementing lineartime modelchecking, and for obtaining many extensions and improvements to this verification method. On the other hand, for branching temporal logic, automatatheoretic techniques have long been thought to introduce an exponential penalty, making them essentially useless for modelchecking. Recently, Bernholtz and Grumberg have shown that this exponential penalty can be avoided, though they did not match the linear complexity of nonautomatatheoretic algorithms. In this paper we show that alternating tree automata are the key to a comprehensive automatatheoretic framework for branching temporal logics. Not only, as was shown by Muller et al., can they be used to obtain optimal decision procedures, but, as we show here, they also make it possible to derive optimal modelchecking algorithms. Moreover, the simple combinatorial structure that emerges from the a...
Structural Operational Semantics
 Handbook of Process Algebra
, 1999
"... Structural Operational Semantics (SOS) provides a framework to give an operational semantics to programming and specification languages, which, because of its intuitive appeal and flexibility, has found considerable application in the theory of concurrent processes. Even though SOS is widely use ..."
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Cited by 148 (19 self)
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Structural Operational Semantics (SOS) provides a framework to give an operational semantics to programming and specification languages, which, because of its intuitive appeal and flexibility, has found considerable application in the theory of concurrent processes. Even though SOS is widely used in programming language semantics at large, some of its most interesting theoretical developments have taken place within concurrency theory. In particular, SOS has been successfully applied as a formal tool to establish results that hold for whole classes of process description languages. The concept of rule format has played a major role in the development of this general theory of process description languages, and several such formats have been proposed in the research literature. This chapter presents an exposition of existing rule formats, and of the rich body of results that are guaranteed to hold for any process description language whose SOS is within one of these formats. As far as possible, the theory is developed for SOS with features like predicates and negative premises.
Combining Deduction and Model Checking into Tableaux and Algorithms for ConversePDL
 Information and Computation
, 1998
"... . This paper presents a prefixed tableaux calculus for Propositional Dynamic Logic with Converse based on a combination of different techniques such as prefixed tableaux for modal logics and model checkers for ¯calculus. We prove the correctness and completeness of the calculus and illustrate its f ..."
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Cited by 66 (7 self)
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. This paper presents a prefixed tableaux calculus for Propositional Dynamic Logic with Converse based on a combination of different techniques such as prefixed tableaux for modal logics and model checkers for ¯calculus. We prove the correctness and completeness of the calculus and illustrate its features. We also discuss the transformation of the tableaux method (naively NEXPTIME) into an EXPTIME algorithm. 1 Introduction Propositional Dynamic Logics (PDLs) are modal logics introduced in [10] to model the evolution of the computation process by describing the properties of states reached by programs during their execution [15, 24, 27]. Over the years, PDLs have been proved to be a valuable formal tool in Computer Science, Logic, Computational Linguistics, and Artificial Intelligence far beyond their original use for program verification (e.g. [4, 12, 14, 15, 24, 23]). In this paper we focus on ConversePDL (CPDL) [10], obtained from the basic logic PDL by adding the converse operat...
EXPTIME tableaux for ALC
 ARTIFICIAL INTELLIGENCE
, 2000
"... The last years have seen two major advances in Knowledge Representation and Reasoning. First, many interesting problems (ranging from Semistructured Data to Linguistics) were shown to be expressible in logics whose main deductive problems are EXPTIMEcomplete. Second, experiments in automated reaso ..."
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Cited by 58 (4 self)
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The last years have seen two major advances in Knowledge Representation and Reasoning. First, many interesting problems (ranging from Semistructured Data to Linguistics) were shown to be expressible in logics whose main deductive problems are EXPTIMEcomplete. Second, experiments in automated reasoning have substantially broadened the meaning of “practical tractability”. Instances of realistic size for PSPACEcomplete problems are now within reach for implemented systems. Still, there is a gap between the reasoning services needed by the expressive logics mentioned above and those provided by the current systems. Indeed, the algorithms based on treeautomata, which are used to prove EXPTIMEcompleteness, require exponential time and space even in simple cases. On the other hand, current algorithms based on tableau methods can take advantage of such cases, but require double exponential time in the worst case. We propose a tableau calculus for the description logic ALC for checking the satisfiability of a concept with respect to a TBox with general axioms, and transform it into the first simple tableaubased decision procedure working in single exponential time. To guarantee the ease of implementation, we also discuss the effects that optimizations (propositional backjumping, simplification, semantic branching, etc.) might have on our complexity result, and introduce a few optimizations ourselves.
Reasoning about Actions and Planning in LTL Action Theories
 In Proc. KR02
, 2002
"... In this paper, we study reasoning about actions and planning with incomplete information in a setting where the dynamic system is specified by adopting Linear Temporal Logic (ltl). Specifically, we study: (i) reasoning about action effects (i.e., projection, historical queries, etc.), in such ..."
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Cited by 30 (8 self)
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In this paper, we study reasoning about actions and planning with incomplete information in a setting where the dynamic system is specified by adopting Linear Temporal Logic (ltl). Specifically, we study: (i) reasoning about action effects (i.e., projection, historical queries, etc.), in such a setting; (ii) when actions can be legally executed, assuming a nonprescriptive approach, where executing an action is possible in a given situation unless forbidden by the system specification; (iii) the problem of finding conformant plans for temporally extended goals that consist of arbitrary ltl formulas, thus allowing for expressing sophisticated dynamic requirements.
What can knowledge representation do for semistructured data
 In Proc. of the 15th Nat. Conf. on Artificial Intelligence (AAAI98
, 1998
"... The problem of modeling semistructured data is important in many application areas such as multimedia data management, biological databases, digital libraries, and data integration. Graph schemas (Buneman et al. 1997) have been proposed recently as a simple and elegant formalism for representing se ..."
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Cited by 27 (9 self)
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The problem of modeling semistructured data is important in many application areas such as multimedia data management, biological databases, digital libraries, and data integration. Graph schemas (Buneman et al. 1997) have been proposed recently as a simple and elegant formalism for representing semistructured data. In this model, schemas are represented as graphs whose edges are labeled with unary formulae of a theory, and the notions of conformance of a database to a schema and of subsumption between two schemas are defined in terms of a simulation relation. Several authors have stressed the need of extending graph schemas with various types of constraints, such as edge existence and constraints on the number of outgoing edges. In this paper we analyze the appropriateness of various knowledge representation formalisms for representing and reasoning about graph schemas extended with constraints. We argue that neither First Order Logic, nor Logic Programming nor Framebased languages are satisfactory for this purpose, and present a solution based on very expressive Description Logics. We provide techniques and complexity analysis for the problem of deciding schema subsumption and conformance in various interesting cases, that differ by the expressive power in the specification of constraints.
Foundations of relational artifacts verification
, 2011
"... Artifacts are entities characterized by data of interest (constituting the state of the artifact) in a given business application, and a lifecycle, which constrains the artifact’s possible evolutions. In this paper we study relational artifacts, where data are represented by a full fledged relation ..."
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Cited by 20 (9 self)
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Artifacts are entities characterized by data of interest (constituting the state of the artifact) in a given business application, and a lifecycle, which constrains the artifact’s possible evolutions. In this paper we study relational artifacts, where data are represented by a full fledged relational database, and the lifecycle is described by a temporal/dynamic formula expressed in µcalculus. We then consider business processes, modeled as a set of condition/action rules, in which the execution of actions (aka tasks, or atomic services) results in new artifact states. We study conformance of such processes wrt the artifact lifecycle as well as verification of temporal/dynamic properties expressed in µcalculus. Notice that such systems are infinitestate in general, hence undecidable. However, inspired by recent literature on database dependencies developed for data exchange, we present a natural restriction that makes such systems finitestate, and the above problems decidable.
Semistructured data with constraints and incomplete information
 In Description Logics
, 1998
"... The problem of modeling semistructured data is important in many application areas such as multimedia data management, biological databases, digital libraries, and data integration. In this paper, we base our work on bdfs, which is a formal and elegant model for semistructured data [Buneman et al., ..."
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Cited by 15 (0 self)
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The problem of modeling semistructured data is important in many application areas such as multimedia data management, biological databases, digital libraries, and data integration. In this paper, we base our work on bdfs, which is a formal and elegant model for semistructured data [Buneman et al., 1997] where schemas are graphs whose edges are labeled with formulae of a theory T. We extend bdfs with the possibility of expressing constraints and dealing with incomplete information. In particular, we consider different types of constraints, and discuss how the expressive power of the constraint language may influence the complexity of checking subsumption between schemas. We then set up a framework for defining bdfs schemas under the assumption that the theory T is not complete. Finally, we propose a new semistructured data model, which extends bdfs with both constraints and incomplete theories. We present a technique for checking subsumption in a setting where both the constraints and the theory are expressed in a very powerful language. 1