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34
Reasoning about Infinite Computations
 Information and Computation
, 1994
"... We investigate extensions of temporal logic by connectives defined by finite automata on infinite words. We consider three different logics, corresponding to three different types of acceptance conditions (finite, looping and repeating) for the automata. It turns out, however, that these logics all ..."
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Cited by 250 (55 self)
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We investigate extensions of temporal logic by connectives defined by finite automata on infinite words. We consider three different logics, corresponding to three different types of acceptance conditions (finite, looping and repeating) for the automata. It turns out, however, that these logics all have the same expressive power and that their decision problems are all PSPACEcomplete. We also investigate connectives defined by alternating automata and show that they do not increase the expressive power of the logic or the complexity of the decision problem. 1 Introduction For many years, logics of programs have been tools for reasoning about the input/output behavior of programs. When dealing with concurrent or nonterminating processes (like operating systems) there is, however, a need to reason about infinite computations. Thus, instead of considering the first and last states of finite computations, we need to consider the infinite sequences of states that the program goes through...
The complexity of set constraints
, 1993
"... Abstract. Set constraints are relations between sets of terms. They have been used extensively in various applications in program analysis and type inference. We present several results on the computational complexity of solving systems of set constraints. The systems we study form a natural complex ..."
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Cited by 67 (11 self)
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Abstract. Set constraints are relations between sets of terms. They have been used extensively in various applications in program analysis and type inference. We present several results on the computational complexity of solving systems of set constraints. The systems we study form a natural complexity hierarchy depending on the form of the constraint language. 1
Partial Derivatives of Regular Expressions and Finite Automata Constructions
 Theoretical Computer Science
, 1995
"... . We introduce a notion of a partial derivative of a regular expression. It is a generalization to the nondeterministic case of the known notion of a derivative invented by Brzozowski. We give a constructive definition of partial derivatives, study their properties, and employ them to develop a new ..."
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Cited by 59 (0 self)
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. We introduce a notion of a partial derivative of a regular expression. It is a generalization to the nondeterministic case of the known notion of a derivative invented by Brzozowski. We give a constructive definition of partial derivatives, study their properties, and employ them to develop a new algorithm for turning regular expressions into relatively small NFA and to provide certain improvements to Brzozowski's algorithm constructing DFA. We report on a prototype implementation of our algorithm constructing NFA and present some examples. Introduction In 1964 Janusz Brzozowski introduced word derivatives of regular expressions and suggested an elegant algorithm turning a regular expression r into a deterministic finite automata (DFA); the main point of the algorithm is that the word derivatives of r serve as states of the resulting DFA [5]. In the following years derivatives were recognized as a quite useful and productive tool. Conway [8] uses derivatives to present various comp...
Decidability of Systems of Set Constraints with Negative Constraints
 INFORMATION AND COMPUTATION
, 1994
"... Set constraints are relations between sets of terms. They have been used extensively in various applications in program analysis and type inference. Recently, several algorithms for solving general systems of positive set constraints have appeared. In this paper we consider systems of mixed posi ..."
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Cited by 54 (10 self)
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Set constraints are relations between sets of terms. They have been used extensively in various applications in program analysis and type inference. Recently, several algorithms for solving general systems of positive set constraints have appeared. In this paper we consider systems of mixed positive and negative constraints, which are considerably more expressive than positive constraints alone. We show that it is decidable whether a given such system has a solution. The proof involves a reduction to a numbertheoretic decision problem that may be of independent interest.
Solving Systems of Set Constraints (Extended Abstract)
 In Seventh Annual IEEE Symposium on Logic in Computer Science
, 1992
"... ) Alexander Aiken Edward L. Wimmers IBM Almaden Research Center 650 Harry Rd. San Jose, CA 95120 phone: 408/9271876 or 9271882 email: lastname@almaden.ibm.com fax: 408/9272100 Abstract Systems of set constraints are a natural formalism for many problems in program analysis. Set constraints ar ..."
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Cited by 31 (0 self)
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) Alexander Aiken Edward L. Wimmers IBM Almaden Research Center 650 Harry Rd. San Jose, CA 95120 phone: 408/9271876 or 9271882 email: lastname@almaden.ibm.com fax: 408/9272100 Abstract Systems of set constraints are a natural formalism for many problems in program analysis. Set constraints are also a generalization of tree automata. We present an algorithm for solving systems of set constraints built from free variables, constructors, and the set operations of intersection, union, and complement. Furthermore, we show that all solutions of such systems can be finitely represented. 1 1 Introduction Set constraints are a natural formalism for describing relationships between sets of terms of a free algebra. A set constraint has the form X ` Y , where X and Y are set expressions. Examples of set expressions are 0 (the empty set), 1 (the set of all terms), ff (a setvalued variable), c(X; Y ) (a constructor application) , and the union, intersection, or complement of set expressi...
Antichains: A new algorithm for checking universality of finite automata
 In Proc. of CAV 2006, LNCS 4144
, 2006
"... Abstract. We propose and evaluate a new algorithm for checking the universality of nondeterministic finite automata. In contrast to the standard algorithm, which uses the subset construction to explicitly determinize the automaton, we keep the determinization step implicit. Our algorithm computes th ..."
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Cited by 30 (14 self)
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Abstract. We propose and evaluate a new algorithm for checking the universality of nondeterministic finite automata. In contrast to the standard algorithm, which uses the subset construction to explicitly determinize the automaton, we keep the determinization step implicit. Our algorithm computes the least fixed point of a monotone function on the lattice of antichains of state sets. We evaluate the performance of our algorithm experimentally using the random automaton model recently proposed by Tabakov and Vardi. We show that on the difficult instances of this probabilistic model, the antichain algorithm outperforms the standard one by several orders of magnitude. We also show how variations of the antichain method can be used for solving the languageinclusion problem for nondeterministic finite automata, and the emptiness problem for alternating finite automata. 1
Rewriting Extended Regular Expressions
, 1993
"... We concider an extened algebra of regular events (languages) with intersection besides the usual operations. This algebra has the structure of a distributive lattice with monotonic operations; the latter property is crucial for some applications. We give a new complete Horn equational axiomatiztion ..."
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Cited by 19 (1 self)
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We concider an extened algebra of regular events (languages) with intersection besides the usual operations. This algebra has the structure of a distributive lattice with monotonic operations; the latter property is crucial for some applications. We give a new complete Horn equational axiomatiztion of the algebra and develop some termrewriting techniques for constructing logical inferences of valid equations. A shorter version of this paper is to appear in the proceedings of Developments in Language Theory, Univ. of Turku, July 1993, published by World Scientific. The present version has been submitted for publication elsewhere. 1 Introduction In this paper we consider an extended algebra of regular events (languages) on a given alphabet with intersection besides the usual operations (union, concatenation, Kleene star, empty, and the regular unit). This algebra has the structure of a distributive lattice (join is union, meet is intersection) with only monotonic operations. The latte...
Recognizing Regular Expressions by means of Dataflow Networks
 In proc. of the 23rd International Colloquium on Automata, Languages, and Programming, (ICALP'96
, 1996
"... . This paper addresses the problem of building a Boolean dataflow network (sequential circuit) recognizing the language described by a regular expression. The main result is that both the construction time and the size of the resulting network are linear with respect to the size of the regular expre ..."
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Cited by 18 (2 self)
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. This paper addresses the problem of building a Boolean dataflow network (sequential circuit) recognizing the language described by a regular expression. The main result is that both the construction time and the size of the resulting network are linear with respect to the size of the regular expression. Introduction "Grep" machine: Let \Sigma be a vocabulary, L be a regular language on \Sigma . A "grep" machine is a machine receiving a sequence s 0 ; s 1 ; : : : ; s n ; : : : of symbols (s i 2 \Sigma ) and computing a sequence b 0 ; b 1 ; : : : ; b n ; : : : of Booleans, such that b n is true if and only if the word s 0 s 1 : : : s n belongs to L 2 . This paper addresses the problem of building a "grep" machine for languages described by regular expressions. This problem is rather classical [4, 11, 10, 3, 1, 2]. We propose a solution which, to our knowledge, is new: Informally, it consists of building, from a regular expression E, a "circuit" (or Boolean dataflow network) explori...
Algebraic rewritings for optimizing regular path queries
 Proc. ICDT ’01
, 2001
"... Rewriting queries using views is a powerful technique that has applications in query optimization, data integration, data warehousing etc. Query rewriting in relational databases is by now rather well investigated. However, in the framework of semistructured data the problem of rewriting has receive ..."
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Cited by 11 (3 self)
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Rewriting queries using views is a powerful technique that has applications in query optimization, data integration, data warehousing etc. Query rewriting in relational databases is by now rather well investigated. However, in the framework of semistructured data the problem of rewriting has received much less attention. In this paper we focus on extracting as much information as possible from algebraic rewritings for the purpose of optimizing regular path queries. The cases when we can find a complete exact rewriting of a query using a set a views are very "ideal." However, there is always information available in the views, even if this information is only partial. We introduce "lower" and "possibility" partial rewritings and provide algorithms for computing them. These rewritings are algebraic in their nature, i.e. we use only the algebraic view definitions for computing the rewritings. This fact makes them a main memory product which can be used for reducing secondary memory and remote access. We give two algorithms for utilizing the partial lower and partial possibility rewritings in the context of query optimization.
LISA: A Specification Language Based on WS2S
, 1998
"... We integrate two concepts from programming languages into a specification language based on WS2S, namely highlevel data structures such as records and recursivelydefined datatypes (WS2S is the weak secondorder monadic logic of two successors). Our integration is based on a new logic whose variabl ..."
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Cited by 10 (1 self)
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We integrate two concepts from programming languages into a specification language based on WS2S, namely highlevel data structures such as records and recursivelydefined datatypes (WS2S is the weak secondorder monadic logic of two successors). Our integration is based on a new logic whose variables range over recordlike trees and an algorithm for translating datatypes into tree automata. We have implemented LISA, a prototype system based on these ideas, which, when coupled with a decision procedure for WS2S like the MONA system, results in a verification tool that supports both highlevel specifications and complexity estimations for the running time of the decision procedure.