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106
Realtime logics: complexity and expressiveness
 INFORMATION AND COMPUTATION
, 1993
"... The theory of the natural numbers with linear order and monadic predicates underlies propositional linear temporal logic. To study temporal logics that are suitable for reasoning about realtime systems, we combine this classical theory of in nite state sequences with a theory of discrete time, via ..."
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Cited by 202 (16 self)
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The theory of the natural numbers with linear order and monadic predicates underlies propositional linear temporal logic. To study temporal logics that are suitable for reasoning about realtime systems, we combine this classical theory of in nite state sequences with a theory of discrete time, via a monotonic function that maps every state to its time. The resulting theory of timed state sequences is shown to be decidable, albeit nonelementary, and its expressive power is characterized by! regular sets. Several more expressive variants are proved to be highly undecidable. This framework allows us to classify a wide variety of realtime logics according to their complexity and expressiveness. Indeed, it follows that most formalisms proposed in the literature cannot be decided. We are, however, able to identify two elementary realtime temporal logics as expressively complete fragments of the theory of timed state sequences, and we present tableaubased decision procedures for checking validity. Consequently, these two formalisms are wellsuited for the speci cation and veri cation of realtime systems.
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.
Discounting the future in systems theory
 In Automata, Languages, and Programming, LNCS 2719
, 2003
"... ..."
Verification of Concurrent Programs: The AutomataTheoretic Framework
 Annals of Pure and Applied Logic
, 1987
"... We present an automatatheoretic framework to the verification of concurrent and nondeterministic programs. The basic idea is that to verify that a program P is correct one writes a program A that receives the computation of P as input and diverges only on incorrect computations of P . Now P is c ..."
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Cited by 47 (3 self)
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We present an automatatheoretic framework to the verification of concurrent and nondeterministic programs. The basic idea is that to verify that a program P is correct one writes a program A that receives the computation of P as input and diverges only on incorrect computations of P . Now P is correct if and only if a program PA , obtained by combining P and A, terminates. We formalize this idea in a framework of !automata with a recursive set of states. This unifies previous works on verification of fair termination and verification of temporal properties. 1 Introduction In this paper we present an automatatheoretic framework that unifies several trends in the area of concurrent program verification. The trends are temporal logic, model checking, automata theory, and fair termination. Let us start with a survey of these trends. In 1977 Pnueli suggested the use of temporal logic in the verification of concurrent programs [Pn77]. The basic motivation is that in the verificat...
Learning via Queries in ...
, 1992
"... We prove that the set of all recursive functions cannot be inferred using firstorder queries in the query language containing extra symbols [+; !]. The proof of this theorem involves a new decidability result about Presburger arithmetic which is of independent interest. Using our machinery, we ..."
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Cited by 35 (11 self)
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We prove that the set of all recursive functions cannot be inferred using firstorder queries in the query language containing extra symbols [+; !]. The proof of this theorem involves a new decidability result about Presburger arithmetic which is of independent interest. Using our machinery, we show that the set of all primitive recursive functions cannot be inferred with a bounded number of mind changes, again using queries in [+; !]. Additionally, we resolve an open question in [7] about passive versus active learning. 1) Introduction This paper presents new results in the area of query inductive inference (introduced in [7]); in addition, there are results of interest in mathematical logic. Inductive inference is the study of inductive machine learning in a theoretical framework. In query inductive inference, we study the ability of a Query Inference Machine 1 Supported, in part, by NSF grants CCR 8803641 and 9020079. 2 Also with IBM Corporation, Application Solutions...
The Regular RealTime Languages
 In Proc. 25th Int. Coll. Automata, Languages, and Programming (ICALP'98
, 1998
"... . A specification formalism for reactive systems defines a class of !languages. We call a specification formalism fully decidable if it is constructively closed under boolean operations and has a decidable satisfiability (nonemptiness) problem. There are two important, robust classes of !languages ..."
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Cited by 35 (3 self)
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. A specification formalism for reactive systems defines a class of !languages. We call a specification formalism fully decidable if it is constructively closed under boolean operations and has a decidable satisfiability (nonemptiness) problem. There are two important, robust classes of !languages that are definable by fully decidable formalisms. The !regular languages are definable by finite automata, or equivalently, by the Sequential Calculus. The counterfree !regular languages are definable by temporal logic, or equivalently, by the firstorder fragment of the Sequential Calculus. The gap between both classes can be closed by finite counting (using automata connectives), or equivalently, by projection (existential secondorder quantification over letters). A specification formalism for realtime systems defines a class of timed !languages, whose letters have realnumbered time stamps. Two popular ways of specifying timing constraints rely on the use of clocks, and on the use...
A practical method for verifying eventdriven software
 In Proceedings of ICSE'99, International Conference on Software Engineering
, 1999
"... Formal verification methods are used only sparingly in software development. The most successful methods to date are based on the use of model checking tools. To use such tools, the user must first define a faithful abstraction of the application (the model), specify how the application interacts wi ..."
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Cited by 33 (0 self)
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Formal verification methods are used only sparingly in software development. The most successful methods to date are based on the use of model checking tools. To use such tools, the user must first define a faithful abstraction of the application (the model), specify how the application interacts with its environment, and then formulate the properties that it should satisfy. Each step in this process can become an obstacle. To complete the verification process successfully often requires specialized knowledge of verification techniques and a considerable investment of time. In this paper we describe a verification method that requires little or no specialized knowledge in model construction. It allows us to extract models mechanically from the source of software applications, securing accuracy. Interface definitions and property specifications have meaningful defaults that can be adjusted when the checking process becomes more refined. All checks can be executed mechanically, even when the application itself continues to evolve. Compared to conventional software testing, the thoroughness of a check of this type is unprecedented.
MONA Version 1.4 User Manual
 Department of Computer Science, University of Aarhus
, 2001
"... Reproduction of all or part of this document is permitted on condition that it is unmodified, includes this copyright notice, and is distributed for free. The MONA tool is available under the GNU General Public License. ..."
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Cited by 32 (1 self)
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Reproduction of all or part of this document is permitted on condition that it is unmodified, includes this copyright notice, and is distributed for free. The MONA tool is available under the GNU General Public License.
The Monadic Theory of Morphic Infinite Words and Generalizations
"... We present new examples of infinite words which have a decidable monadic theory. Formally, we consider structures hN; <; P i which expand the ordering hN;
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Cited by 28 (7 self)
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We present new examples of infinite words which have a decidable monadic theory. Formally, we consider structures hN; <; P i which expand the ordering hN; <i of the natural numbers by a unary predicate P ; the corresponding infinite word is the characteristic 01sequence xP of P . We show that for a morphic predicate P the associated monadic secondorder theory MThhN; <; P i is decidable, thus extending results of Elgot and Rabin (1966) and Maes (1999). The solution is obtained in the framework of semigroup theory, which is then connected to the known automata theoretic approach of Elgot and Rabin. Finally, a large class of predicates P is exhibited such that the monadic theory MThhN; <; P i is decidable, which unifies and extends the previously known examples.
Bounded Model Construction for Monadic SecondOrder Logics
 In 12th International Conference on ComputerAided Verification (CAV’00), number 1855 in LNCS
, 2000
"... The monadic logics M2LStr and WS1S have been successfully used for verification, although they are nonelementary decidable. Motivated by ideas from bounded model checking, we investigate procedures for bounded model construction for these logics. The problem is, given a formula and a bound k, does ..."
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Cited by 28 (2 self)
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The monadic logics M2LStr and WS1S have been successfully used for verification, although they are nonelementary decidable. Motivated by ideas from bounded model checking, we investigate procedures for bounded model construction for these logics. The problem is, given a formula and a bound k, does there exist a word model for of length k. We give a bounded model construction algorithm for M2LStr that runs in a time exponential in k. For WS1S, we prove a negative result: bounded model construction is as hard as validity checking, i.e., it is nonelementary. From this, negative results for other monadic logics, such as S1S, follow. We present too preliminary tests using a SATbased implementation of bounded model construction; for certain problem classes it can find counterexamples substantially faster than automatabased decision procedures.