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Multiple counters automata, safety analysis and Presburger arithmetic
, 1998
"... We consider automata with counters whose values are updated according to signals sent by the environment. A transition can be fired only if the values of the counters satisfy some guards (the guards of the transition). We consider guards of the form y i #y j +c i;j where y i is either x 0 i or ..."
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Cited by 89 (1 self)
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We consider automata with counters whose values are updated according to signals sent by the environment. A transition can be fired only if the values of the counters satisfy some guards (the guards of the transition). We consider guards of the form y i #y j +c i;j where y i is either x 0 i or x i , the values of the counter i respectively after and before the transition, and # is any relational symbol in f=; ; ; ?; !g. We show that the set of possible counter values which can be reached after any number of iterations of a loop is definable in the additive theory of N (or Z or R depending on the type of the counters). This result can be used for the safety analysis of multiple counters automata. 1 Introduction Finite state automata provide a nice framework for the verification of reactive systems. Their main advantage is the equivalence between recognizability and definability in some decidable logic (e.g. Monadic Second Order Logic or some of its fragments such as tempora...
The Standardization of Message Sequence Charts
 Computer Networks and ISDN Systems
, 1993
"... In this paper the most relevant issues of the standardization of the Message Sequence Chart (MSC) language within the CCITT Study Group X are discussed. The history of the new MSC recommendation Z.120 is sketched. Different types of diagrams which are closely related to MSCs are compared, since they ..."
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Cited by 83 (11 self)
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In this paper the most relevant issues of the standardization of the Message Sequence Chart (MSC) language within the CCITT Study Group X are discussed. The history of the new MSC recommendation Z.120 is sketched. Different types of diagrams which are closely related to MSCs are compared, since they build the basis for the MSC language. We distinguish these diagrams from the standardized MSC language by using the term Sequence Charts (SCs). Subsequently, the MSC language is introduced and several approaches towards a forthcoming formal MSC semantics are presented. 1 Introduction Sequence Charts (SCs) are a widespread means for the graphical visualization of selected system runs (traces) within communication systems. They can be viewed as a special trace language, which mainly concentrates on sending and consumption of messages by synchronously or asynchronously communicating processes. Obviously, main advantage of an SC is its clear graphical layout (e.g. fig. 1, 2), which immediately...
Symbolic model checking for probabilistic processes
 IN PROCEEDINGS OF ICALP '97
, 1997
"... We introduce a symbolic model checking procedure for Probabilistic Computation Tree Logic PCTL over labelled Markov chains as models. Model checking for probabilistic logics typically involves solving linear equation systems in order to ascertain the probability of a given formula holding in a stat ..."
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Cited by 83 (29 self)
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We introduce a symbolic model checking procedure for Probabilistic Computation Tree Logic PCTL over labelled Markov chains as models. Model checking for probabilistic logics typically involves solving linear equation systems in order to ascertain the probability of a given formula holding in a state. Our algorithm is based on the idea of representing the matrices used in the linear equation systems by MultiTerminal Binary Decision Diagrams (MTBDDs) introduced in Clarke et al [14]. Our procedure, based on the algorithm used by Hansson and Jonsson [24], uses BDDs to represent formulas and MTBDDs to represent Markov chains, and is efficient because it avoids explicit state space construction. A PCTL model checker is being implemented in Verus [9].
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 77 (9 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.
Monadic Datalog and the Expressive Power of Languages for Web Information Extraction
 J. ACM
, 2002
"... Research on information extraction from Web pages (wrapping) has seen much activity in recent times (particularly systems implementations), but little work has been done on formally studying the expressiveness of the formalisms proposed or on the theoretical foundations of wrapping. In this paper, w ..."
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Cited by 75 (11 self)
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Research on information extraction from Web pages (wrapping) has seen much activity in recent times (particularly systems implementations), but little work has been done on formally studying the expressiveness of the formalisms proposed or on the theoretical foundations of wrapping. In this paper, we first study monadic datalog as a wrapping language (over ranked or unranked tree structures). Using previous work by Neven and Schwentick, we show that this simple language is equivalent to full monadic second order logic (MSO) in its ability to specify wrappers. We believe that MSO has the right expressiveness required for Web information extraction and thus propose MSO as a yardstick for evaluating and comparing wrappers. Using the above result, we study the kernel fragment Elog of the Elog wrapping language used in the Lixto system (a visual wrapper generator). The striking fact here is that Elog exactly captures MSO, yet is easier to use. Indeed, programs in this language can be entirely visually specified. We also formally compare Elog to other wrapping languages proposed in the literature.
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 74 (11 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
Monadic Queries over TreeStructured Data
, 2002
"... Monadic query languages over trees currently receive considerable interest in the database community, as the problem of selecting nodes from a tree is the most basic and widespread database query problem in the context of XML. Partly a survey of recent work done by the authors and their group on log ..."
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Cited by 71 (9 self)
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Monadic query languages over trees currently receive considerable interest in the database community, as the problem of selecting nodes from a tree is the most basic and widespread database query problem in the context of XML. Partly a survey of recent work done by the authors and their group on logical query languages for this problem and their expressiveness, this paper provides a number of new results related to the complexity of such languages over socalled axis relations (such as "child" or "descendant") which are motivated by their presence in the XPath standard or by their utility for data extraction (wrapping).
Diophantine Equations, Presburger Arithmetic and Finite Automata
, 1996
"... . We show that the use of finite automata provides a decision procedure for Presburger Arithmetic with optimal worst case complexity. Introduction Solving linear equations and inequations with integer coefficients in the set Nof nonnegative integer plays an important role in many areas of computer ..."
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Cited by 71 (1 self)
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. We show that the use of finite automata provides a decision procedure for Presburger Arithmetic with optimal worst case complexity. Introduction Solving linear equations and inequations with integer coefficients in the set Nof nonnegative integer plays an important role in many areas of computer science, such as associative commutative unification, constraint logic programming, compiler optimization,... The firstorder theory of Nwith addition 0 and 1 is known as Presburger arithmetic and has been shown decidable as early as in 1929 [5]. The special case of linear Diophantine equations has been studied even earlier [2]. Much work has been devoted recently to improve the effectiveness of known methods, as well as in designing new efficient algorithms [3, 1, ?, ?]. For example, E, Domenjoud and A.P. Tomas in [?] study old methods of Elliot and Mac Mahon [2, 4], improving their algorithms and extending so as to be able to solve more complex systems including inequations () and disequ...
Planning Control Rules for Reactive Agents
 Artificial Intelligence
, 1997
"... A traditional approach for planning is to evaluate goal statements over state trajectories modeling predicted behaviors of an agent. This paper describes a powerful extension of this approach for handling complex goals for reactive agents. We describe goals by using a modal temporal logic that can e ..."
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Cited by 70 (6 self)
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A traditional approach for planning is to evaluate goal statements over state trajectories modeling predicted behaviors of an agent. This paper describes a powerful extension of this approach for handling complex goals for reactive agents. We describe goals by using a modal temporal logic that can express quite complex time, safety, and liveness constraints. Our method is based on an incremental planner algorithm that generates a reactive plan by computing a sequence of partially satisfactory reactive plans converging to a completely satisfactory one. Partial satisfaction means that an agent controlled by the plan accomplishes its goal only for some environment events. Complete satisfaction means that the agent accomplishes its goal whatever environment events occur during the execution of the plan. As such, our planner can be stopped at any time to yield a useful plan. An implemented prototype is used to evaluate our planner on empirical problems. Keywords: Planning, control, reactiv...
MONA Implementation Secrets
, 2000
"... The MONA tool provides an implementation of the decision procedures for the logics WS1S and WS2S. It has been used for numerous applications, and it is remarkably efficient in practice, even though it faces a theoretically nonelementary worstcase complexity. The implementation has matured over a p ..."
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Cited by 70 (6 self)
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The MONA tool provides an implementation of the decision procedures for the logics WS1S and WS2S. It has been used for numerous applications, and it is remarkably efficient in practice, even though it faces a theoretically nonelementary worstcase complexity. The implementation has matured over a period of six years. Compared to the first naive version, the present tool is faster by several orders of magnitude. This speedup is obtained from many different contributions working on all levels of the compilation and execution of formulas. We present a selection of implementation "secrets" that have been discovered and tested over the years, including formula reductions, DAGification, guided tree automata, threevalued logic, eager minimization, BDDbased automata representations, and cacheconscious data structures. We describe these techniques and quantify their respective effects by experimenting with separate versions of the MONA tool that in turn omit each of them.