Modal Logic and Process Algebra

UCL Discovery
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Nemeti 2. Process Algebra with Feedback J. Baeten, J. Bergstra, and Gh. Stefanescu 3. Frame-Based Process Logics J. Bergstra and A. Ponse 4. Re-interpreting the Modal m-Calculus Marcello M. Bonsangue and Marta Z.

Bialgebraic methods and modal logic in structural operational semantics

Kwiatkowska 5. Groote and S. This work is concerned with regular languages defined over large alphabets, either infinite or just too large to be expressed enumeratively. We define a generic model where transitions are labeled by elements of a finite partition of the alphabet. We have implemented this algorithm and we demonstrate its behavior where the alphabet is a subset of the natural or real numbers.

Modal Logic and Process Algebra by Alban Ponse, Maarten de Rijke, Yde Venema -

We sketch the extension of the algorithm to a class of languages over partially ordered alphabets. A weighted automaton is functional if any two accepting runs on the same finite word have the same value. In this paper, we investigate functional weighted automata for four different measures: the sum, the mean, the discounted sum of weights along edges and the ratio between rewards and costs. On the positive side, we show that functionality is decidable for the four measures.

Furthermore, the existential and universal threshold problems, the language inclusion problem and the equivalence problem are all decidable when the weighted automata are functional. On the negative side, we also study the quantitative extension of the realizability problem and show that it is undecidable for sum, mean and ratio.

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We finally show how to decide whether the language associated with a given functional automaton can be defined with a deterministic one, for sum, mean and discounted sum. We propose a method for compositional verification to address the state space explosion problem inherent to model-checking timed systems with a large number of components.

The main challenge is to obtain pertinent global timing constraints from the timings in the components alone. To this end, we make use of auxiliary clocks to automatically generate new invariants which capture the constraints induced by the synchronisations between components.

Modal Logic and Process Algebra a Bisimulation Perspective

The method has been implemented in the RTD-Finder tool and successfully experimented on several benchmarks. Partial functions and domination Chong, C. The current work introduces the notion of pdominant sets and studies their recursion-theoretic properties. No weakly 2-generic set is pdominant while there are pdominant 1-generic sets below K.

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There is a low r. A general method is established to derive a ground-complete axiomatization for a weak semantics from such an axiomatization for its concrete counterpart, in the context of the process algebra BCCS. This transformation moreover preserves omega-completeness. It is applicable to semantics at least as coarse as impossible futures semantics. As an application, ground- and omega-complete axiomatizations are derived for weak failures, completed trace and trace semantics.

We then present a finite, sound, ground-complete axiomatization for the concrete impossible futures preorder, which implies a finite, sound, ground-complete axiomatization for the weak impossible futures preorder. In contrast, we prove that no finite, sound axiomatization for BCCS modulo concrete and weak impossible futures equivalence is ground-complete. If the alphabet of actions is infinite, then the aforementioned ground-complete axiomatizations are shown to be omega-complete.

1. Logic Lecture: Introduction to Modal Logic

Positive modal logic was introduced in an influential paper of Dunn as the positive fragment of standard modal logic. His completeness result consists of an axiomatization that derives all modal formulas that are valid on all Kripke frames and are built only from atomic propositions, conjunction, disjunction, box and diamond. In this paper, we provide a coalgebraic analysis of this theorem, which not only gives a conceptual proof based on duality theory, but also generalizes Dunn's result from Kripke frames to coalgebras for weak-pullback preserving functors.

Functors arising in this way are said to have a presentation in discrete arities. VeriFast is a leading research prototype tool for the sound modular verification of safety and correctness properties of single-threaded and multithreaded C and Java programs. It has been used as a vehicle for exploration and validation of novel program verification techniques and for industrial case studies; it has served well at a number of program verification competitions; and it has been used for teaching by multiple teachers independent of the authors.

However, until now, while VeriFast's operation has been described informally in a number of publications, and specific verification techniques have been formalized, a clear and precise exposition of how VeriFast works has not yet appeared.

In this article we present for the first time a formal definition and soundness proof of a core subset of the VeriFast program verification approach. We study decidability of verification problems for timed automata extended with unbounded discrete data structures.

More detailed, we extend timed automata with a pushdown stack. In this way, we obtain a strong model that may for instance be used to model real-time programs with procedure calls. It is long known that the reachability problem for this model is decidable. The goal of this paper is to identify subclasses of timed pushdown automata for which the language inclusion problem and related problems are decidable. Weak upper topologies and duality for cones Keimel, Klaus. In functional analysis it is well known that every linear functional defined on the dual of a locally convex vector space which is continuous for the weak topology is the evaluation at a uniquely determined point of the given vector space.

Schroeder and A. Simpson have obtained a similar result for lower semicontinuous linear functionals on the cone of all Scott-continuous valuations on a topological space endowed with the weak upper topology, an asymmetric version of the weak topology. This result has given rise to several proofs, originally by the Schroeder and Simpson themselves and, more recently, by the author of these Notes and by J. The proofs developed from very technical arguments to more and more conceptual ones. The present Note continues on this line, presenting a conceptual approach inspired by classical functional analysis which may prove useful in other situations.

A rooted planar map is a connected graph embedded in the 2-sphere, with one edge marked and assigned an orientation. A term of the pure lambda calculus is said to be linear if every variable is used exactly once, normal if it contains no beta-redexes, and planar if it is linear and the use of variables moreover follows a deterministic stack discipline.

We begin by showing that the sequence counting normal planar lambda terms by a natural notion of size coincides with the sequence originally computed by Tutte counting rooted planar maps by number of edges. Next, we explain how to apply the machinery of string diagrams to derive a graphical language for normal planar lambda terms, extracted from the semantics of linear lambda calculus in symmetric monoidal closed categories equipped with a linear reflexive object or a linear reflexive pair.

A new hierarchy of "exact" unification types is introduced, motivated by the study of admissible rules for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by instantiation, but rather by inclusion over the corresponding sets of unified identities. Minimal complete sets of unifiers under this new preordering always have a smaller or equal cardinality than those provided by the standard instantiation preordering, and in significant cases a dramatic reduction may be observed.

In particular, the classes of distributive lattices, idempotent semigroups, and MV-algebras, which all have nullary unification type, have unitary or finitary exact type.