2013
DOI: 10.2168/lmcs-9(2:4)2013
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Two Variable vs. Linear Temporal Logic in Model Checking and Games

Abstract: Abstract. Model checking linear-time properties expressed in first-order logic has nonelementary complexity, and thus various restricted logical languages are employed. In this paper we consider two such restricted specification logics, linear temporal logic (LTL) and two-variable first-order logic (FO 2 ). LTL is more expressive but FO 2 can be more succinct, and hence it is not clear which should be easier to verify. We take a comprehensive look at the issue, giving a comparison of verification problems for … Show more

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Cited by 4 publications
(3 citation statements)
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“…To the best of our knowledge, verifying parametric properties on MCs has not been considered so far. The closest related works are on combining two-variable FO with LTL for MDPs by Benedikt et al [13] and the computation of quantiles by Ummels and Baier [14].…”
Section: Introductionmentioning
confidence: 99%
“…To the best of our knowledge, verifying parametric properties on MCs has not been considered so far. The closest related works are on combining two-variable FO with LTL for MDPs by Benedikt et al [13] and the computation of quantiles by Ummels and Baier [14].…”
Section: Introductionmentioning
confidence: 99%
“…In the second case we conclude that D is recurrent. If D is, in addition, accepting, then we can use the result of our iterative computation to simplify the linear system (5): we compute a cut vector µ and a scalar c > 0 so that c µ ⊤ y(i) = 1, and replace all equations in (5) with variables from ζ D on the left-hand side by ζ D = c y(i). This algorithm is justified by the following two lemmas, combined with Lemma 10(2).…”
Section: Analyzing Sccsmentioning
confidence: 99%
“…Furthermore we use our procedure to show that the model checking problem of finite Markov chains against unambiguous automata lies in the complexity class NC: the subclass of P comprising those problems solvable in poly-logarithmic time by a parallel random-access machine using polynomially many processors. The existence of a polynomial-time algorithm for model checking Markov chains against UBA has previously been claimed in [5,4,32] (see also [31]). However these previous works share a common fundamental error-see [3] for details and counterexamples to incorrect claims in these works.…”
Section: Introductionmentioning
confidence: 97%