Results 1  10
of
38
Twovariable logic on words with data
 In LICS
, 2006
"... Abstract — In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been already considered in the realm of semistructured data, timed automata and extended temporal logics. It is shown that satisfiability for the twovariable ..."
Abstract

Cited by 66 (13 self)
 Add to MetaCart
Abstract — In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been already considered in the realm of semistructured data, timed automata and extended temporal logics. It is shown that satisfiability for the twovariable firstorder logic FO 2 (∼, <, +1) is decidable over finite and over infinite data words, where ∼ is a binary predicate testing the data value equality and +1,< are the usual successor and order predicates. The complexity of the problem is at least as hard as Petri net reachability. Several extensions of the logic are considered, some remain decidable while some are undecidable. I.
Classifying Discrete Temporal Properties
 Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science (STACS 99), Lecture Notes in Computer Science 1563, SpringerVerlag
, 1999
"... This paper surveys recent results on the classification of discrete temporal properties, gives an introduction to the methods that have been developed to obtain them, and explains the connections to the theory of finite automata, the theory of nite semigroups, and to firstorder logic. ..."
Abstract

Cited by 38 (0 self)
 Add to MetaCart
This paper surveys recent results on the classification of discrete temporal properties, gives an introduction to the methods that have been developed to obtain them, and explains the connections to the theory of finite automata, the theory of nite semigroups, and to firstorder logic.
Diamonds Are Forever: The Variety DA
 Semigroups, Algorithms, Automata and Languages, Coimbra (Portugal) 2001
, 2002
"... We survey different characterizations (algebraic, combinatorial,... ..."
Abstract

Cited by 27 (5 self)
 Add to MetaCart
We survey different characterizations (algebraic, combinatorial,...
Partiallyordered Twoway Automata: A New Characterization of DA
 In Developments in Language Theory
, 2001
"... In this paper, we consider nite automata with the restriction that whenever the automaton leaves a state it never returns to it. ..."
Abstract

Cited by 21 (3 self)
 Add to MetaCart
In this paper, we consider nite automata with the restriction that whenever the automaton leaves a state it never returns to it.
TWOWAY UNARY TEMPORAL LOGIC OVER TREES
, 2009
"... We consider a temporal logic EF + F −1 for unranked, unordered finite trees. The logic has two operators: EFϕ, which says “in some proper descendant ϕ holds”, and F −1 ϕ, which says “in some proper ancestor ϕ holds”. We present an algorithm for deciding if a regular language of unranked finite tree ..."
Abstract

Cited by 20 (3 self)
 Add to MetaCart
We consider a temporal logic EF + F −1 for unranked, unordered finite trees. The logic has two operators: EFϕ, which says “in some proper descendant ϕ holds”, and F −1 ϕ, which says “in some proper ancestor ϕ holds”. We present an algorithm for deciding if a regular language of unranked finite trees can be expressed in EF+F −1. The algorithm uses a characterization expressed in terms of forest algebras.
Forest Algebras
"... There are at least as many interesting classes of regular tree languages as there are of regular word languages. However, much less is known about the former ones. In particular, very few decidable characterizations of tree language classes are known. For words, most known characterizations are obta ..."
Abstract

Cited by 18 (8 self)
 Add to MetaCart
There are at least as many interesting classes of regular tree languages as there are of regular word languages. However, much less is known about the former ones. In particular, very few decidable characterizations of tree language classes are known. For words, most known characterizations are obtained using algebra. With this in mind, the present paper proposes an algebraic framework for classifying regular languages of finite unranked labeled trees. If in a transformation semigroup we assume that the set being acted upon has a semigroup structure, then the transformation semigroup can be used to recognize languages of unranked trees. This observation allows us to examine the relationship connecting tree languages with standard algebraic concepts such as aperiodicity idempotency, or commutativity. The new algebraic setting is used to give several examples of decidable algebraic characterizations.
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 ..."
Abstract

Cited by 16 (6 self)
 Add to MetaCart
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.
Nesting Until and Since in Linear Temporal Logic
 Syst
, 2002
"... We provide an effective characterization of the "untilsince hierarchy" of linear temporal logic, that is, we show how to compute for a given temporal property the minimal nesting depth in "until" and "since" required to express it. This settles the most prominent classification problem for linear t ..."
Abstract

Cited by 12 (3 self)
 Add to MetaCart
We provide an effective characterization of the "untilsince hierarchy" of linear temporal logic, that is, we show how to compute for a given temporal property the minimal nesting depth in "until" and "since" required to express it. This settles the most prominent classification problem for linear temporal logic. Our characterization of the individual levels of the "untilsince hierarchy" is algebraic: for each n, we present a decidable class of finite semigroups and show that a temporal property is expressible with nesting depth at most n if and only if the syntactic semigroup of the formal language associated with the property belongs to the class provided. The core of our algebraic characterization is a new description of substitution in linear temporal logic in terms of block products of finite semigroups.
Structure Theorem and Strict Alternation Hierarchy for FO² on Words
"... It is wellknown that every firstorder property on words is expressible using at most three variables. The subclass of properties expressible with only two variables is also quite interesting and wellstudied. We prove precise structure theorems that characterize the exact expressive power of first ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
It is wellknown that every firstorder property on words is expressible using at most three variables. The subclass of properties expressible with only two variables is also quite interesting and wellstudied. We prove precise structure theorems that characterize the exact expressive power of firstorder logic with two variables on words. Our results apply to both the case with and without a successor relation. For both languages, our structure theorems show exactly what is expressible using a given quantifier depth, n, and using m blocks of alternating quantifiers, for any m ≤ n. Using these characterizations, we prove, among other results, that there is a strict hierarchy of alternating quantifiers for both languages. The question whether there was such a hierarchy had been completely open. As another consequence of our structural results, we show that satisfiability for firstorder logic with two variables without successor, which is NEXPcomplete in general, becomes NPcomplete once we only consider alphabets of a bounded size.