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54
Finite Model Theory and Descriptive Complexity
, 2002
"... This is a survey on the relationship between logical definability and computational complexity on finite structures. Particular emphasis is given to gamebased evaluation algorithms for various logical formalisms and to logics capturing complexity classes. In addition to the ..."
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Cited by 27 (7 self)
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This is a survey on the relationship between logical definability and computational complexity on finite structures. Particular emphasis is given to gamebased evaluation algorithms for various logical formalisms and to logics capturing complexity classes. In addition to the
Policy monitoring in firstorder temporal logic
 In CAV
, 2010
"... Abstract. We present an approach to monitoring system policies. As a specification language, we use an expressive fragment of a temporal logic, which can be effectively monitored. We report on case studies in security and compliance monitoring and use these to show the adequacy of our specification ..."
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Cited by 24 (0 self)
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Abstract. We present an approach to monitoring system policies. As a specification language, we use an expressive fragment of a temporal logic, which can be effectively monitored. We report on case studies in security and compliance monitoring and use these to show the adequacy of our specification language for naturally expressing complex, realistic policies and the practical feasibility of monitoring these policies using our monitoring algorithm. 1
Runtime Monitoring of Metric Firstorder Temporal Properties
"... ABSTRACT. We introduce a novel approach to the runtime monitoring of complex system properties. Inparticular,wepresentanonlinealgorithmforasafetyfragmentofmetricfirstordertemporal logic that is considerably more expressive than the logics supported by prior monitoring methods. Ourapproach,basedonau ..."
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Cited by 24 (12 self)
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ABSTRACT. We introduce a novel approach to the runtime monitoring of complex system properties. Inparticular,wepresentanonlinealgorithmforasafetyfragmentofmetricfirstordertemporal logic that is considerably more expressive than the logics supported by prior monitoring methods. Ourapproach,basedonautomaticstructures,allowstheunrestricteduseofnegation,universaland existential quantification over infinite domains, and the arbitrary nesting of both past and bounded future operators. Moreover, we show how to optimize our approach for the common case where structuresconsistofonlyfiniterelations,overpossiblyinfinitedomains. Underanadditionalrestriction, we prove that the space consumed by our monitor is polynomially bounded by the cardinality of the data appearing intheprocessed prefixof thetemporal structure being monitored.
Describing groups
 Bull. Symb. Logic
"... Abstract. Two ways of describing a group are considered. 1. A group is finiteautomaton presentable if its elements can be represented by strings over a finite alphabet, in such a way that the set of representing strings and the group operation can be recognized by finite automata. 2. An infinite f.g ..."
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Abstract. Two ways of describing a group are considered. 1. A group is finiteautomaton presentable if its elements can be represented by strings over a finite alphabet, in such a way that the set of representing strings and the group operation can be recognized by finite automata. 2. An infinite f.g. group is quasifinitely axiomatizable if there is a description consisting of a single firstorder sentence, together with the information that the group is finitely generated. In the first part of the paper we survey examples of FApresentable groups, but also discuss theorems restricting this class. In the second part, we give examples of quasifinitely axiomatizable groups, consider the algebraic content of the notion, and compare it to the notion of a group which is a prime model. We also show that if a structure is biinterpretable in parameters with the ring of integers, then it is prime and
Bounds in ωregularity
"... We consider an extension of ωregular expressions where two new variants of the Kleene star L ∗ are added: L B and L S. These exponents act as the standard star, but restrict the number of iterations to be bounded (for L B) or to tend toward infinity (for L S). These expressions can define languages ..."
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Cited by 11 (4 self)
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We consider an extension of ωregular expressions where two new variants of the Kleene star L ∗ are added: L B and L S. These exponents act as the standard star, but restrict the number of iterations to be bounded (for L B) or to tend toward infinity (for L S). These expressions can define languages that are not ωregular. We develop a theory for these languages. We study the decidability and closure questions. We also define an equivalent automaton model, extending Büchi automata. This culminates with a — partial — complementation result. 1
Cardinality and counting quantifiers on omegaautomatic structures
 In Proceedings of the 25th International Symposium on Theoretical Aspects of Computer Science, STACS 2008
, 2008
"... Abstract. We investigate structures that can be represented by omegaautomata, so called omegaautomatic structures, and prove that relations defined over such structures in firstorder logic expanded by the firstorder quantifiers ‘there exist at most ℵ0 many’, ’there exist finitely many ’ and ’the ..."
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Abstract. We investigate structures that can be represented by omegaautomata, so called omegaautomatic structures, and prove that relations defined over such structures in firstorder logic expanded by the firstorder quantifiers ‘there exist at most ℵ0 many’, ’there exist finitely many ’ and ’there exist k modulo m many ’ are omegaregular. The proof identifies certain algebraic properties of omegasemigroups. As a consequence an omegaregular equivalence relation of countable index has an omegaregular set of representatives. This implies Blumensath’s conjecture that a countable structure with an ωautomatic presentation can be represented using automata on finite words. This also complements a very recent result of Hjörth, Khoussainov, Montalban and Nies showing that there is an omegaautomatic structure which has no injective presentation. 1.
TRANSFORMING STRUCTURES BY SET INTERPRETATIONS
"... We consider a new kind of interpretation over relational structures: finite sets interpretations. Those interpretations are defined by weak monadic secondorder (WMSO) formulas with free set variables. They transform a given structure into a structure with a domain consisting of finite sets of eleme ..."
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Cited by 10 (2 self)
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We consider a new kind of interpretation over relational structures: finite sets interpretations. Those interpretations are defined by weak monadic secondorder (WMSO) formulas with free set variables. They transform a given structure into a structure with a domain consisting of finite sets of elements of the orignal structure. The definition of these interpretations directly implies that they send structures with a decidable WMSO theory to structures with a decidable firstorder theory. In this paper, we investigate the expressive power of such interpretations applied to infinite deterministic trees. The results can be used in the study of automatic and treeautomatic structures.
Algorithmic metatheorems for decidable LTL model checking over infinite systems
"... By algorithmic metatheorems for a model checking problem P over infinitestate systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a large family of classes of infinite systems. Such results n ..."
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By algorithmic metatheorems for a model checking problem P over infinitestate systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a large family of classes of infinite systems. Such results normally start with a powerful formalism F of infinitestate systems, over which P is undecidable, and assert decidability when is restricted by means of an extra “semantic condition ” C. We prove various algorithmic metatheorems for the problems of model checking LTL and its two common fragments LTL(Fs,Gs) and LTLdet over the expressive class of word/tree automatic transition systems, which are generated by synchronized finitestate transducers operating on finite words and trees. We present numerous applications, where we derive (in a unified manner) many known and previously unknown decidability and complexity results of model checking LTL and its fragments over specific classes of infinitestate systems including pushdown systems; prefixrecognizable systems; reversalbounded counter systems with discrete clocks and a free counter; concurrent pushdown systems with a bounded number of contextswitches; various subclasses of Petri nets; weakly extended PAprocesses; and weakly extended groundtree rewrite systems. In all cases, we are able to derive optimal (or near optimal) complexity. Finally, we pinpoint the exact locations in the arithmetic and analytic hierarchies of the problem of checking a relevant semantic condition and the LTL model checking problems over all word/tree automatic systems.
Modelchecking CTL ∗ over flat Presburger counter systems
 JANCL
"... ABSTRACT. This paper studies modelchecking of fragments and extensions of CTL * on infinitestate counter systems, where the states are vectors of integers and the transitions are determined by means of relations definable within Presburger arithmetic. In general, reachability properties of counter ..."
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Cited by 8 (5 self)
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ABSTRACT. This paper studies modelchecking of fragments and extensions of CTL * on infinitestate counter systems, where the states are vectors of integers and the transitions are determined by means of relations definable within Presburger arithmetic. In general, reachability properties of counter systems are undecidable, but we have identified a natural class of admissible counter systems (ACS) for which we show that the quantification over paths in CTL * can be simulated by quantification over tuples of natural numbers, eventually allowing translation of the whole PresburgerCTL * into Presburger arithmetic, thereby enabling effective model checking. We provide evidence that our results are close to optimal with respect to the class of counter systems described above.