We examine when a model checker for a propositional program logic can be used for checking another propositional program logic in spite of lack of expressive power of the first logic. We prove that (1) a branching time Computation Tree Logic CTL, (2) the propositional μ-Calculus of D. Kozen μC , and (3) the second-order propositional program logic 2M of C. Stirling enjoy the equal model checkin...

In our previous study, we defined the semantics of modal μ-calculus on minplus algebra N∞ and developed a model-checking algorithm. N∞ is the set of all natural numbers and infinity (∞), and has two operations min and plus. In the semantics, disjunctions are interpreted by min and conjunctions by plus. This semantics allows interesting properties of a Kripke structure, such as the shortest path...

For more than two decades, researchers have tried to develop tools and algorithms to increase the dependability of computerized systems. All the verification techniques can be gathered under the generic name of formal methods, the most famous and successful one being certainly model checking [SCH 99], which consists in building a mathematical model of a system S, and then check that it satisfie...

let φ be a w  -continuous homomorphism from a dual banach algebra to c. the notion of φ-connes amenability is studied and some characterizations is given. a type of diagonal for dual banach algebras is dened. it is proved that the existence of such a diagonal is equivalent to φ-connes amenability. it is also shown that φ-connes amenability is equivalent to so-called φ-splitting of a certain s...

We introduce a technique for component-based program synthesis that relies on searching for a target program and its proof of correctness simultaneously using a purely constraint-based approach, rather than exploring the space of possible programs in an enumerate-and-check loop. Our approach solves a synthesis problem by checking satisfiability of an ∃∃ constraint φ, whereas traditional program...

This technical note describes a monotone and continuous fixpoint operator to compute the answer sets of programs with aggregates. The fixpoint operator relies on the notion of aggregate solution. Under certain conditions, this operator behaves identically to the three-valued immediate consequence operator Φ P for aggregate programs, independently proposed in (Pelov 2004; Pelov et al. 2004). Thi...

We consider the problem of checking whether a proposed invariant φ expressed in first-order logic with quantifier alternation is inductive, i.e. preserved by a piece of code. While the problem is undecidable, modern SMT solvers can sometimes solve it automatically. However they employ powerful quantifier instantiation methods that may diverge, especially when φ is not preserved. A notable diffi...

Model-checking gained wide popularity for analyzing software and hardware systems. However, even when the desired property holds, the property or the model may still require fixing. For example, a property φ: “on all paths, a request is followed by an acknowledgment”, may hold because no requests have been generated. Vacuity detection has been proposed to address the above problem. This techniq...

We consider the problem of verifying stochastic models of biochemical networks against behavioral properties expressed in temporal logic terms. Exact probabilistic verification approaches such as, for example, CSL/PCTL model checking, are undermined by a huge computational demand which rule them out for most real case studies. Less demanding approaches, such as statistical model checking, estim...