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MONA: Monadic SecondOrder Logic in Practice
 IN PRACTICE, IN TOOLS AND ALGORITHMS FOR THE CONSTRUCTION AND ANALYSIS OF SYSTEMS, FIRST INTERNATIONAL WORKSHOP, TACAS '95, LNCS 1019
, 1995
"... The purpose of this article is to introduce Monadic Secondorder Logic as a practical means of specifying regularity. The logic is a highly succinct alternative to the use of regular expressions. We have built a tool MONA, which acts as a decision procedure and as a translator to finitestate au ..."
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Cited by 148 (20 self)
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The purpose of this article is to introduce Monadic Secondorder Logic as a practical means of specifying regularity. The logic is a highly succinct alternative to the use of regular expressions. We have built a tool MONA, which acts as a decision procedure and as a translator to finitestate automata. The tool is based on new algorithms for minimizing finitestate automata that use binary decision diagrams (BDDs) to represent transition functions in compressed form. A byproduct of this work is a new bottomup algorithm to reduce BDDs in linear time without hashing. The potential
On the Structure of Inductive Reasoning: Circular and TreeShaped Proofs in the µCalculus
 IN PROCEEDINGS OF FOSSACS 2003
, 2003
"... In this paper we study induction in the context of the firstorder µcalculus with explicit approximations. We present and compare two Gentzenstyle proof systems each using a different type of induction. The first is ..."
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Cited by 22 (3 self)
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In this paper we study induction in the context of the firstorder µcalculus with explicit approximations. We present and compare two Gentzenstyle proof systems each using a different type of induction. The first is
Decidable Call by Need Computations in Term Rewriting (Extended Abstract)
 Proc. of 14th International Conference on Automated Deduction, CADE'97, LNAI 1249:418
, 1997
"... ) Ir#ne Durand Universit# de Bordeaux I, France Aart Middeldorp University of Tsukuba, Japan Abstract In this paper we study decidable approximations to call by need computations to normal and rootstable forms in term rewriting. We obtain uniform decidability proofs by making use of elementary ..."
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Cited by 17 (3 self)
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) Ir#ne Durand Universit# de Bordeaux I, France Aart Middeldorp University of Tsukuba, Japan Abstract In this paper we study decidable approximations to call by need computations to normal and rootstable forms in term rewriting. We obtain uniform decidability proofs by making use of elementary tree automata techniques. Surprisingly, by avoiding complicated concepts like index and sequentiality we are able to cover much larger classes of term rewriting systems. 1 Introduction The following theorem of Huet and L#vy [8] forms the basis of all results on optimal normalizing reduction strategies for orthogonal term rewriting systems (TRSs): every reducible term contains a needed redex, i.e., a redex which is contracted in every rewrite sequence to normal form, and repeated contraction of needed redexes results in a normal form, if the term under consideration has a normal form. Unfortunately, needed redexes are not computable in general. Hence, in order to obtain a computable optimal...
T (2001) Model checking LTL properties of highlevel Petri nets with fairness constraints
 In: Proc. 22nd Conference on Application and Theory of Petri Nets, LNCS 2075
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A graphtheoretic generalization of the least common subsumer and the most specific concept in the description logic EL
, 2004
"... In two previous papers we have investigates the problem of computing the least common subsumer (lcs) and the most specific concept (msc) for the description logic EL in the presence of terminological cycles that are interpreted with descriptive semantics, which is the usual firstorder semantics for ..."
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Cited by 7 (0 self)
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In two previous papers we have investigates the problem of computing the least common subsumer (lcs) and the most specific concept (msc) for the description logic EL in the presence of terminological cycles that are interpreted with descriptive semantics, which is the usual firstorder semantics for description logics. In this setting, neither the lcs nor the msc needs to exist. We were able to characterize the cases in which the lcs/msc exists, but it was not clear whether this characterization yields decidability of the existence problem. In the present paper, we develop a common graphtheoretic generalization of these characterizations, and show that the resulting property is indeed decidable, thus yielding decidability of the existence of the lcs and the msc. This is achieved by expressing the property in monadic secondorder logic on in¯nite trees. We also show that, if it exists, then the lcs/msc can be computed in polynomial time.
Timed Alternating Tree Automata: The AutomataTheoretic Solution to the TCTL Model Checking Problem
 In Proc. 26th ICALP, LNCS 1644
, 1999
"... We introduce timed alternating tree automata as a natural extension of timed automata for the purpose of solving the model checking problem for timed computation tree logic (TCTL) following the automatatheoretic approach. This settles a problem posed by Henzinger, Kupferman, and Vardi. ..."
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Cited by 5 (0 self)
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We introduce timed alternating tree automata as a natural extension of timed automata for the purpose of solving the model checking problem for timed computation tree logic (TCTL) following the automatatheoretic approach. This settles a problem posed by Henzinger, Kupferman, and Vardi.
Methodology Of Dynamical Analysis Of SDL Programs Using Predicate/Transition Nets
, 1997
"... The rapid increase of parallel and distributed systems has brought new problems related to the correctness of the systems. In this work the automatic verification tool EMMA is presented, which uses Predicate/Transition nets to model TNSDL programs. The verification is based on reachability analysis ..."
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The rapid increase of parallel and distributed systems has brought new problems related to the correctness of the systems. In this work the automatic verification tool EMMA is presented, which uses Predicate/Transition nets to model TNSDL programs. The verification is based on reachability analysis with the PROD analyzer. Several methods to avoid state space explosion are discussed, e.g. model optimization, advanced state space generation algorithms and direct TNSDL program manipulation. The emphasis in this work will be on model optimizations for industrial TNSDL programs, but nonexhaustive methods are also considered. Key principles used in the modeling of TNSDL programs are also explained. In the EMMA project the complete TNSDL language has been modeled. The difference between the model and the implementation is small, because both are generated automatically from the same TNSDL specication. The results of the reachability analysis are translated back to TNSDL making the tool easier to use for specialists not acquainted with net theory.
On Infinite CSP's
"... We present a new generalization of Constraint Satisfaction Problems (CSP's) to allow infinitely (or unboundedly) many indexed variables. The indices of variables are specified in a firstorder decidable theory. We call this generalization Infinite CSP's (ICSP's). Applications of ICSP ..."
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Cited by 3 (1 self)
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We present a new generalization of Constraint Satisfaction Problems (CSP's) to allow infinitely (or unboundedly) many indexed variables. The indices of variables are specified in a firstorder decidable theory. We call this generalization Infinite CSP's (ICSP's). Applications of ICSP include problems in which the number of variables is unknown a priori, and optimization problems wrt the number of variables satisfying a given finite set of constraints. We shall study...
On Innite CSP's
"... Abstract We present a new generalization of Constraint Satisfaction Problems (CSP's) to allow innitely (or unboundedly) many indexed variables. The indices of variables are specied in a rstorder decidable theory. We call this generalization Innite CSP's (ICSP's). Applications of ICSP ..."
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Abstract We present a new generalization of Constraint Satisfaction Problems (CSP's) to allow innitely (or unboundedly) many indexed variables. The indices of variables are specied in a rstorder decidable theory. We call this generalization Innite CSP's (ICSP's). Applications of ICSP include problems in which the number of variables is unknown a priori, and optimization problems wrt the number of variables satisfying a given nite set of constraints. We shall study the decidability of the satisability problem for ICSP's wrt (a) the rstorder theory specifying the indices of variables and (b) the dimension of the indices. We rst show that (1) if the indices are onedimensional and specied in the theory of the natural numbers with linear order (the theory of (N; 0; succ; <)) then the satisability problem is decidable. We then prove that, in constrast to (1), (2) if we move to the twodimensional case then the satisability problem is undecidable for indices specied in (N; 0; succ; <) and even in (N; 0; succ). Finally, we show that, in constrast to (1) and (2), already in the onedimensional case (3) if we also allow addition, we get undecidability. I.e., if the onedimensional indices are specied in Presburger arithmetic (i.e., the theory of (N; 0; succ; <;+)) then satisability is undecidable. 1