Nondeterminism in algebraic specifications and algebraic programs

"Nondeterminism in Algebraic Specifications and Algebraic Programs" presents a mathematical theory for the integration of three concepts: non-determinism, axiomatic specification and term rewriting. For non-deterministic programs, an algebraic specification language is provided which admits the application of automated tools based on term rewriting techniques. This general framework is used to explore connections between logic programming and algebraic programming. Examples from various areas of computer science are given, including results of computer experiments with a prototypical implementation. This book should be of interest to readers working within several fields of theoretical computer science, from algebraic specification theory to formal descriptions of distributed systems

No complete linear term rewriting system for propositional logic

International audienceRecently it has been observed that the set of all sound linear inference rules in propositional logic is already coNP-complete, i.e. that every Boolean tautology can be written as a (left-and right-) linear rewrite rule. This raises the question of whether there is a rewriting system on linear terms of propositional logic that is sound and complete for the set of all such rewrite rules. We show in this paper that, as long as reduction steps are polynomial-time decidable, such a rewriting system does not exist unless coNP = NP. We draw tools and concepts from term rewriting, Boolean function theory and graph theory in order to access the required intermediate results. At the same time we make several connections between these areas that, to our knowledge, have not yet been presented and constitute a rich theoretical framework for reasoning about linear TRSs for propositional logic. 1998 ACM Subject Classification F.4 Mathematical Logic and Formal Language

A Graph Rewriting Approach for Transformational Design of Digital Systems

Transformational design integrates design and verification. It combines “correctness by construction” and design creativity by the use of pre-proven behaviour preserving transformations as design steps. The formal aspects of this methodology are hidden in the transformations. A constraint is the availability of a design representation with a compositional formal semantics. Graph representations are useful design representations because of their visualisation of design information. In this paper graph rewriting theory, as developed in the last twenty years in mathematics, is shown to be a useful basis for a formal framework for transformational design. The semantic aspects of graphs which are no part of graph rewriting theory are included by the use of attributed graphs. The used attribute algebra, table algebra, is a relation algebra derived from database theory. The combination of graph rewriting, table algebra and transformational design is new

Comparing and evaluating extended Lambek calculi

Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a logical theory). However, though it was successful in giving at least a basic treatment of many linguistic phenomena, it was also clear that a slightly more expressive logical calculus was needed for many other cases. Therefore, many extensions and variants of the Lambek calculus have been proposed, since the eighties and up until the present day. As a result, there is now a large class of calculi, each with its own empirical successes and theoretical results, but also each with its own logical primitives. This raises the question: how do we compare and evaluate these different logical formalisms? To answer this question, I present two unifying frameworks for these extended Lambek calculi. Both are proof net calculi with graph contraction criteria. The first calculus is a very general system: you specify the structure of your sequents and it gives you the connectives and contractions which correspond to it. The calculus can be extended with structural rules, which translate directly into graph rewrite rules. The second calculus is first-order (multiplicative intuitionistic) linear logic, which turns out to have several other, independently proposed extensions of the Lambek calculus as fragments. I will illustrate the use of each calculus in building bridges between analyses proposed in different frameworks, in highlighting differences and in helping to identify problems.Comment: Empirical advances in categorial grammars, Aug 2015, Barcelona, Spain. 201

Extending the Real-Time Maude Semantics of Ptolemy to Hierarchical DE Models

This paper extends our Real-Time Maude formalization of the semantics of flat Ptolemy II discrete-event (DE) models to hierarchical models, including modal models. This is a challenging task that requires combining synchronous fixed-point computations with hierarchical structure. The synthesis of a Real-Time Maude verification model from a Ptolemy II DE model, and the formal verification of the synthesized model in Real-Time Maude, have been integrated into Ptolemy II, enabling a model-engineering process that combines the convenience of Ptolemy II DE modeling and simulation with formal verification in Real-Time Maude.Comment: In Proceedings RTRTS 2010, arXiv:1009.398

Full Semantics Preservation in Model Transformation – A Comparison of Proof Techniques

Model transformation is a prime technique in modern, model-driven software design. One of the most challenging issues is to show that the semantics of the models is not affected by the transformation. So far, there is hardly any research into this issue, in particular in those cases where the source and target languages are different.\ud \ud In this paper, we are using two different state-of-the-art proof techniques (explicit bisimulation construction versus borrowed contexts) to show bisimilarity preservation of a given model transformation between two simple (self-defined) languages, both of which are equipped with a graph transformation-based operational semantics. The contrast between these proof techniques is interesting because they are based on different model transformation strategies: triple graph grammars versus in situ transformation. We proceed to compare the proofs and discuss scalability to a more realistic setting.\u