We show that a 2-variable integer program, defined by m constraints involving coefficients with at most φ bits can be solved with O(m+ φ) arithmetic operations on rational numbers of size O(φ). This result closes the gap between the running time of two-variable integer programming with the sum of the running times of the Euclidean algorithm on φ-bit integers and the problem of checking feasibil...

The model-checking problem is to decide, given a formula φ and an interpretation M , whether M satisfies φ, written M |= φ. Model-checking algorithms for temporal logics were initially developed with finite models (such as models of hardware) in mind so that M |= φ is decidable. As interest grew in model-checking infinite systems, other approaches were developed based on approximating the model...

We propose an approach to perform efficient model-checking of μ-calculus formulae on modular Petri nets. Given a formula φ, each module can be analysed separately, possibly yielding a conclusion about the truth value of φ on the global system. When no conclusion can be drawn locally, a minimal state space preserving φ is computed for the module and can be incrementally composed with others, thu...

Model checking is a method to validate the correct functioning of a piece of hardor software. Specifications are expressed in temporal logic. A model checking algorithm determines automatically whether or not the checked model satisfies a given specification by examining the model’s state space. In their basic form model checking algorithms explore the state space exhaustively. As the number of...

We define memory-efficient certificates for μ-calculus model checking problems based on the well-known correspondence of μ-calculus model checking with winning certain parity games. Winning strategies can be independently checked, in low polynomial time, by observing that there is no reachable strongly connected component in the graph of the parity game whose largest priority is odd. Winning st...

The model checking problem for propositional dynamic logic (PDL) over message sequence charts (MSCs) and communicating finite state machines (CFMs) asks, given a channel bound B, a PDL formula φ and a CFM C, whether every existentially B-bounded MSC M accepted by C satisfies φ. Recently, it was shown that this problem is PSPACEcomplete. In the present work, we consider CRPDL over MSCs which is ...

Recently, complexity issues related to the decidability of the μ-calculus, when the universal and existential quantifiers are augmented with graded modalities, have been investigated by Kupfermann, Sattler and Vardi ([19]). Graded modalities refer to the use of the universal and existential quantifiers with the added capability to express the concept of at least k or all but k, for a non-negati...

We introduce a definition of model checking games for the full branching time logic CTL∗ and sketch a proof of their correctness. These games are a helpful technique for using model checking in the verification of concurrent systems, because they may not only show that a specified property is violated, but also why it is. 1 Verification of Concurrent Systems Mathematically, model checking is th...

This paper introduces the logic cpCTL, which extends the probabilistic temporal logic pCTL with conditional probability, allowing one to express that the probability that φ is true given that ψ is true is at least a. We interpret cpCTL over Markov Chain and Markov Decision Processes. While model checking cpCTL over Markov Chains can be done with existing techniques, those techniques do not carr...

The model-checking problem for a logic L is the problem of decidig for a given formula φ ∈ L and structure A whether the formula is true in the structure, i.e. whether A |= φ. Model-checking for logics such as First-Order Logic (FO) or Monadic Second-Order Logic (MSO) has been studied intensively in the literature, especially in the context of algorithmic meta-theorems within the framework of p...