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A survey on small fragments of firstorder logic over finite words
 International Journal of Foundations of Computer Science
, 2008
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Comparing Workflow Specification Languages: A Matter of Views
, 2011
"... We address the problem of comparing the expressiveness of workflow specification formalisms using a notion of view of a workflow. Views allow to compare widely different workflow systems by mapping them to a common representation capturing the observables relevant to the comparison. Using this frame ..."
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We address the problem of comparing the expressiveness of workflow specification formalisms using a notion of view of a workflow. Views allow to compare widely different workflow systems by mapping them to a common representation capturing the observables relevant to the comparison. Using this framework, we compare the expressiveness of several workflow specification mechanisms, including automata, temporal constraints, and preandpost conditions, with XML and relational databases as underlying datamodels. One surprising result shows the considerable power of static constraints to simulate apparently much richer workflow control mechanisms.
ON LOGICAL HIERARCHIES WITHIN FO2DEFINABLE LANGUAGES
"... Abstract. We consider the class of languages defined in the 2variable fragment of the firstorder logic of the linear order. Many interesting characterizations of this class are known, as well as the fact that restricting the number of quantifier alternations yields an infinite hierarchy whose le ..."
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Abstract. We consider the class of languages defined in the 2variable fragment of the firstorder logic of the linear order. Many interesting characterizations of this class are known, as well as the fact that restricting the number of quantifier alternations yields an infinite hierarchy whose levels are varieties of languages (and hence admit an algebraic characterization). Using this algebraic approach, we show that the quantifier alternation hierarchy inside FO2[<] is decidable within one unit. For this purpose, we relate each level of the hierarchy with decidable varieties of languages, which can be defined in terms of iterated deterministic and codeterministic products. A crucial notion in this process is that of condensed rankers, a refinement of the rankers of Weis and Immerman and the turtle languages of Schwentick, Thérien and Vollmer. Many important properties of systems are modeled by finite automata. Frequently, the formal languages induced by these systems are definable
Separating Regular Languages with FirstOrder Logic ∗
"... Given two languages, a separator is a third language that contains the first one and is disjoint from the second one. We investigate the following decision problem: given two regular input languages of finite words, decide whether there exists a firstorder definable separator. We prove that in orde ..."
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Given two languages, a separator is a third language that contains the first one and is disjoint from the second one. We investigate the following decision problem: given two regular input languages of finite words, decide whether there exists a firstorder definable separator. We prove that in order to answer this question, sufficient information can be extracted from semigroups recognizing the input languages, using a fixpoint computation. This yields an EXPTIME algorithm for checking firstorder separability. Moreover, the correctness proof of this algorithm yields a stronger result, namely a description of a possible separator. Finally, we prove that this technique can be generalized to answer the same question for regular languages of infinite words.
An introduction to finite automata and their connection to logic
 of Professor Priti Shankar. Foreword by Reinhard Wilhelm. Hackensack, NJ: World Scientific; Bangalore: IISc Press. IISc Research Monographs Series 2, 3–43 (2012). (Cited on pages 19 and 67
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On regular temporal logics with past
 In Proceedings of the 36th International Colloquium on Automata, Languages, and Programming (ICALP), volume 5556 of Lect. Notes Comput. Sci
"... Abstract. The IEEE standardized Property Specification Language, PSL for short, extends the wellknown lineartime temporal logic LTL with socalled semiextended regular expressions. PSL and the closely related SystemVerilog Assertions, SVA for short, are increasingly used in many phases of the har ..."
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Abstract. The IEEE standardized Property Specification Language, PSL for short, extends the wellknown lineartime temporal logic LTL with socalled semiextended regular expressions. PSL and the closely related SystemVerilog Assertions, SVA for short, are increasingly used in many phases of the hardware design cycle, from specification to verification. In this paper, we extend the common core of these specification languages with past operators. We name this extension RTL. Although all ωregular properties are expressible in PSL, SVA, and RTL, past operators often allow one to specify properties more naturally and concisely. In fact, we show that RTL is exponentially more succinct than the cores of PSL and SVA. Furthermore, we present a translation of RTL into languageequivalent nondeterministic Büchi automata, which is based on novel constructions for 2way alternating automata. Our translation has almost the same worstcase complexity in terms of the size of the resulting nondeterministic Büchi automata as the existing translations for PSL and SVA. Consequently, the satisfiability and the modelchecking problem for RTL fall into the same complexity classes as the corresponding problems for PSL and SVA. From the translation it also follows that the blowup of translating RTL formulas into initially equivalent PSL/SVA formulas is at most triply exponential. 1
On the Expressivity of RoCTL*
, 2009
"... RoCTL * was proposed to model robustness in concurrent systems. RoCTL * extended CTL * with the addition of Obligatory and Robustly operators, which quantify over failurefree paths and paths with one more failure respectively. Whether RoCTL * is more expressive than CTL * has remained an open probl ..."
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RoCTL * was proposed to model robustness in concurrent systems. RoCTL * extended CTL * with the addition of Obligatory and Robustly operators, which quantify over failurefree paths and paths with one more failure respectively. Whether RoCTL * is more expressive than CTL * has remained an open problem since the RoCTL * logic was proposed. We use the equivalence of LTL to counterfree automata to show that RoCTL * is expressively equivalent to CTL*; the translation to CTL * provides the first model checking procedure for RoCTL*. However, we show that RoCTL * is relatively succinct as all satisfaction preserving translations into CTL * are nonelementary in length. Draft:
The semantics of feature models via formal languages: a computational hierarchy for feature models
, 2014
"... The GSDLAB technical reports are published as a means to ensure timely dissemination of scholarly and technical work on a noncommercial basis. Copyright and all rights therein are maintained by the authors or by other copyright holders, notwithstanding that they have offered their works here electr ..."
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The GSDLAB technical reports are published as a means to ensure timely dissemination of scholarly and technical work on a noncommercial basis. Copyright and all rights therein are maintained by the authors or by other copyright holders, notwithstanding that they have offered their works here electronically. It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author’s copyright. These works may not be reposted without the explicit permission of the copyright holder.
Firstorder Fragments with Successor over Infinite Words∗
"... We consider fragments of firstorder logic and as models we allow finite and infinite words simultaneously. The only binary relations apart from equality are order comparison < and the successor predicate +1. We give characterizations of the fragments Σ2 = Σ2[<,+1] and FO2 = FO2[<,+1] in t ..."
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We consider fragments of firstorder logic and as models we allow finite and infinite words simultaneously. The only binary relations apart from equality are order comparison < and the successor predicate +1. We give characterizations of the fragments Σ2 = Σ2[<,+1] and FO2 = FO2[<,+1] in terms of algebraic and topological properties. To this end we introduce the factor topology over infinite words. It turns out that a language L is in FO2 ∩Σ2 if and only if L is the interior of an FO2 language. Symmetrically, a language is in FO2 ∩Π2 if and only if it is the topological closure of an FO2 language. The fragment ∆2 = Σ2∩Π2 contains exactly the clopen languages in FO2. In particular, over infinite words ∆2 is a strict subclass of FO2. Our characterizations yield decidability of the membership problem for all these fragments over finite and infinite words; and as a corollary we also obtain decidability for infinite words. Moreover, we give a new decidable algebraic characterization of dotdepth 3/2 over finite words. Decidability of dotdepth 3/2 over finite words was first shown by Glaßer and Schmitz in STACS 2000, and decidability of the membership problem for FO2 over infinite words was shown 1998 by Wilke in his habilitation thesis whereas decidability of Σ2 over infinite words is new.