In the automata theoretic approach to model checking, checking a state-space S against a linear-time property φ can be done in O(|S| × 2) time. When model checking under n strong fairness hypotheses expressed as a Generalized Büchi automaton, this complexity becomes O(|S| × 2). Here we describe an algorithm to check the emptiness of Streett automata, which allows model checking under n strong f...

We present QMC, a one-sided error Monte Carlo decision procedure for the LTL model-checking problem S |= φ. Besides serving as a randomized algorithm for LTL model checking, QMC delivers quantitative information about the likelihood that S |= φ. In particular, given a specification S of a finite-state system, an LTL formula φ, and parameters and δ, QMC performs random sampling to compute an est...

In this paper we develop an approach to model-checking for timed automata via reachability testing. As our specification formalism, we consider a dense-time logic with clocks. This logic may be used to express safety and bounded liveness properties of real-time systems. We show how to automatically synthesize, for every logical formula φ, a socalled test automaton Tφ in such a way that checking...

Since 3-SAT is NP-complete, checking if a given assignment satisfies φ can be (trivially) accomplished in polynomial time, but finding such an assignment or proving that φ is unsatisfiable requires exponential time in general. Letting m, n, and l be (respectively) the number of clauses, variables, and literals in φ, the naive “try everything” or “guess and check” algorithm runs in O(2n ∗ l) tim...

ing TCTL Formulas Abstraction predicates are extracted from the timed-bounded modalities of the TCTL formula A new clock variable zi is introduced for every time-bounded operator Example: φ = EG<2 p ∧ A[qU≤4 r] Set of predicates: Ψφ = {z1 < 2 } {{ } ψ1 , z2 ≤ 4 } {{ } ψ2 } Abstract CTL formula: φ̂ = EG(p∧ψ1) ∧ A[qU (r∧ψ2)] Lazy Approximation – p.6 Soundness and Completeness Basis predicates: Set...

Given a model M and a temporal logic formula φ[?], where ? is a placeholder, the query checking problem, as defined for the case of CTL by Chan in 2000, is to find the strongest propositional formula f such that M |= φ[? ← f ]. The motivation for solving this problem is, among other things, to get insight on the model. We consider various objectives to the LTL query-checking problem, and study ...

The standard technique for LTL model checking (M φ) consists on translating the negation of the LTL specification, φ, into a Büchi automaton Aφ, and then on checking if the product M Aφ has an empty language. The efforts to maximize the efficiency of this process have so far concentrated on developing translation algorithms producing Büchi automata which are “as small as possible”, under the im...

We propose predicate abstraction as a means for verifying a rich class of safety and liveness properties for dense real-time systems. First, we define a restricted semantics of timed systems which is observationally equivalent to the standard semantics in that it validates the same set of μ-calculus formulas without a next-step operator. Then, we recast the model checking problem S |= φ for a t...

Branching-time temporal logics have proved to be an extraordinarily successful tool in the formal specification and verification of distributed systems. Much of their success stems from the tractability of the model checking problem for the branching time logic ctl, which has made it possible to implement tools that allow designers to automatically verify that systems satisfy requirements expre...