Results 1  10
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23
On the Expressive Power of Temporal Logic
 J. COMPUT. SYSTEM SCI
, 1993
"... We study the expressive power of linear propositional temporal logic interpreted on finite sequences or words. We first give a transparent proof of the fact that a formal language is expressible in this logic if and only if its syntactic semigroup is finite and aperiodic. This gives an effective ..."
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Cited by 42 (4 self)
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We study the expressive power of linear propositional temporal logic interpreted on finite sequences or words. We first give a transparent proof of the fact that a formal language is expressible in this logic if and only if its syntactic semigroup is finite and aperiodic. This gives an effective algorithm to decide whether a given rational language is expressible. Our main result states a similar condition for the "restricted" temporal logic (RTL), obtained by discarding the "until" operator. A formal language is RTLexpressible if and only if its syntactic semigroup is finite and satisfies a certain simple algebraic condition. This leads
Piecewise testable tree languages
"... This paper presents a decidable characterization of tree languages that can be defined by a boolean combination of Σ1 formulas. This is a tree extension of the Simon theorem, which says that a string language can be defined by a boolean combination of Σ1 formulas if and only if its syntactic monoid ..."
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Cited by 16 (6 self)
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This paper presents a decidable characterization of tree languages that can be defined by a boolean combination of Σ1 formulas. This is a tree extension of the Simon theorem, which says that a string language can be defined by a boolean combination of Σ1 formulas if and only if its syntactic monoid is Jtrivial.
The Descriptive Complexity Approach to LOGCFL
, 1998
"... Building upon the known generalizedquantifierbased firstorder characterization of LOGCFL, we lay the groundwork for a deeper investigation. Specifically, we examine subclasses of LOGCFL arising from varying the arity and nesting of groupoidal quantifiers. Our work extends the elaborate theory ..."
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Cited by 11 (5 self)
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Building upon the known generalizedquantifierbased firstorder characterization of LOGCFL, we lay the groundwork for a deeper investigation. Specifically, we examine subclasses of LOGCFL arising from varying the arity and nesting of groupoidal quantifiers. Our work extends the elaborate theory relating monoidal quantifiers to NC and its subclasses. In the absence of the BIT predicate, we resolve the main issues: we show in particular that no single outermost unary groupoidal quantifier with FO can capture all the contextfree languages, and we obtain the surprising result that a variant of Greibach's "hardest contextfree language" is LOGCFLcomplete under quantifierfree BITfree projections. We then prove that FO with unary groupoidal quantifiers is strictly more expressive with the BIT predicate than without. Considering a particular groupoidal quantifier, we prove that firstorder logic with majority of pairs is strictly more expressive than firstorder with major...
PSPACEcomplete problems for subgroups of free groups and inverse finite automata
, 2000
"... We investigate the complexity of algorithmic problems on finitely generated subgroups of free groups. Margolis and Meakin showed how a finite monoid Synt(H) can be canonically and e#ectively associated with such a subgroup H. We show that H is pure (that is, closed under radical) if and only if Synt ..."
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Cited by 10 (2 self)
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We investigate the complexity of algorithmic problems on finitely generated subgroups of free groups. Margolis and Meakin showed how a finite monoid Synt(H) can be canonically and e#ectively associated with such a subgroup H. We show that H is pure (that is, closed under radical) if and only if Synt(H) is aperiodic. We also show that testing for this property of H is pspacecomplete. In the process, we show that certain problems about finite automata which are pspacecomplete in general remain pspacecomplete when restricted to injective and inverse automata (with single accept state), whereas they are known to be in NC for permutation automata (with single accept state). We are concerned with the solution and the complexity of algorithmic problems about finitely generated subgroups of free groups. Our main results are that the problem of deciding purity for a finitely generated subgroup of a free group is decidable, and that it is pspacecomplete. Our techniques rely largely on autom...
Firstorder definable languages
 Logic and Automata: History and Perspectives, Texts in Logic and Games
, 2008
"... We give an essentially selfcontained presentation of some principal results for firstorder definable languages over finite and infinite words. We introduce the notion of a counterfree Büchi automaton; and we relate counterfreeness to aperiodicity and to the notion of very weak alternation. We al ..."
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Cited by 9 (2 self)
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We give an essentially selfcontained presentation of some principal results for firstorder definable languages over finite and infinite words. We introduce the notion of a counterfree Büchi automaton; and we relate counterfreeness to aperiodicity and to the notion of very weak alternation. We also show that aperiodicity of a regular ∞language can be decided in polynomial space, if the language is specified by some Büchi automaton. 1
Some Results on the Generalized StarHeight Problem
, 2001
"... We prove some results related to the generalized starheight problem. In this problem, as opposed to the restricted starheight problem, complementation is considered as a basic operator. We first show that the class of languages of starheight n is closed under certain operations (left and right qu ..."
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Cited by 7 (4 self)
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We prove some results related to the generalized starheight problem. In this problem, as opposed to the restricted starheight problem, complementation is considered as a basic operator. We first show that the class of languages of starheight n is closed under certain operations (left and right quotients, inverse alphabetic morphisms, injective starfree substitutions). It is known that languages recognized by a commutative group are of starheight 1. We extend this result to nilpotent groups of class 2 and to the groups that divide a semidirect product of a commutative group by (Z=2Z) n . In the same direction, we show that one of the languages that was conjectured to be of star height 2 during the past ten years, is in fact of star height 1. Next we show that if a rational language L is recognized by a monoid of the variety generated by wreath products of the form M (G N ), where M and N are aperiodic monoids, and G is a commutative group, then L is of starheight...
Some Algorithmic Problems for Pseudovarieties
 Publ. Math. Debrecen
, 1996
"... Several algorithmic problems for pseudovarieties and their relationships are studied. This includes the usual membership problem and the computability of pointlike subsets of finite semigroups. Some of these problems afford equivalent formulations involving topological separation properties in fr ..."
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Cited by 6 (5 self)
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Several algorithmic problems for pseudovarieties and their relationships are studied. This includes the usual membership problem and the computability of pointlike subsets of finite semigroups. Some of these problems afford equivalent formulations involving topological separation properties in free profinite semigroups. Several examples are considered and, as an application, a decidability result for joins is proved. 1. Introduction Perhaps the three most celebrated results relating the theories of formal languages and finite semigroups are: Schutzenberger's characterization of starfree languages as those whose syntactic semigroups are finite and aperiodic [19]; Simon's characterization of piecewise testable languages as those whose syntactic semigroups are finite and Jtrivial [20]; and Brzozowski and Simon / McNaughton 's characterization of locally testable languages as those whose syntactic semigroups are finite local semilattices [7, 15]. These results led Eilenberg [9] to ...
The expressive power of existential firstorder sentences of Büchi's sequential calculus
"... The aim of this paper is to study the rstorder theory of the successor, interpreted on nite words. More speci cally, we are interested in the hierarchy based on quanti er alternations (or n hierarchy). It was known (Thomas, 1982) that this hierarchy collapses at level 2, but the expressive po ..."
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Cited by 5 (0 self)
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The aim of this paper is to study the rstorder theory of the successor, interpreted on nite words. More speci cally, we are interested in the hierarchy based on quanti er alternations (or n hierarchy). It was known (Thomas, 1982) that this hierarchy collapses at level 2, but the expressive power of the lower levels was not characterized eectively. We give a semigroup theoretic description of the expressive power of B 1 , the boolean combinations of existential formulas. We also give an O(n ) time algorithm to decide whether the language accepted by a deterministic nstate automaton is expressible by a rst order sentence (respectively a B 1 sentence).
The Expressive Power of Existential First Order Sentences of Büchi's Sequential Calculus
"... this paper is to study the first order theory of the successor, interpreted on finite words. More specifically, we complete the study of the hierarchy based on quantifier alternations (or \Sigma nhierarchy). It was known (Thomas, 1982) that this hierarchy collapses at level 2, but the expressive po ..."
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Cited by 5 (1 self)
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this paper is to study the first order theory of the successor, interpreted on finite words. More specifically, we complete the study of the hierarchy based on quantifier alternations (or \Sigma nhierarchy). It was known (Thomas, 1982) that this hierarchy collapses at level 2, but the expressive power of the lower levels was not characterized effectively. We give a semigroup theoretic description of the expressive power of \Sigma 1 , the existential formulas, and B\Sigma 1 , the boolean combinations of existential formulas. Our characterization is algebraic and makes use of the syntactic semigroup, but contrary to a number of results in this field, is not in the scope of Eilenberg's variety theorem, since B\Sigma 1 definable languages are not closed under residuals