Polynomial Invariants for Affine Programs

We exhibit an algorithm to compute the strongest polynomial (or algebraic) invariants that hold at each location of a given affine program (i.e., a program having only non-deterministic (as opposed to conditional) branching and all of whose assignments are given by affine expressions). Our main tool is an algebraic result of independent interest: given a finite set of rational square matrices of the same dimension, we show how to compute the Zariski closure of the semigroup that they generate

Automated verification of refinement laws

Demonic refinement algebras are variants of Kleene algebras. Introduced by von Wright as a light-weight variant of the refinement calculus, their intended semantics are positively disjunctive predicate transformers, and their calculus is entirely within first-order equational logic. So, for the first time, off-the-shelf automated theorem proving (ATP) becomes available for refinement proofs. We used ATP to verify a toolkit of basic refinement laws. Based on this toolkit, we then verified two classical complex refinement laws for action systems by ATP: a data refinement law and Back's atomicity refinement law. We also present a refinement law for infinite loops that has been discovered through automated analysis. Our proof experiments not only demonstrate that refinement can effectively be automated, they also compare eleven different ATP systems and suggest that program verification with variants of Kleene algebras yields interesting theorem proving benchmarks. Finally, we apply hypothesis learning techniques that seem indispensable for automating more complex proofs

Model-Based Adaptation of Software Communicating via FIFO Buffers

Software Adaptation is a non-intrusive solution for composing black-box components or services (peers) whose individual functionality is as required for the new system, but that present interface mismatch, which leads to deadlock or other undesirable behaviour when combined. Adaptation techniques aim at automatically generating new components called adapters. All the interactions among peers pass through the adapter, which acts as an orchestrator and makes the involved peers work correctly together by compensating for mismatch. Most of the existing solutions in this field assume that peers interact synchronously using rendezvous communication. However, many application areas rely on asynchronous communication models where peers interact exchanging messages via buffers. Generating adapters in this context becomes a difficult problem because peers may exhibit cyclic behaviour, and their composition often results in infinite systems. In this paper, we present a method for automatically generating adapters in asynchronous environments where peers interact using FIFO buffers.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Automatic enumeration of regular objects

We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These differential equations are then used to determine the initial counting sequence and for asymptotic analysis. The key tool is the scalar product for symmetric functions and that this operation preserves D-finiteness.Comment: Corrected for readability; To appear in the Journal of Integer Sequence

Computing Equilibria of Semi-algebraic Economies Using Triangular Decomposition and Real Solution Classification

In this paper, we are concerned with the problem of determining the existence of multiple equilibria in economic models. We propose a general and complete approach for identifying multiplicities of equilibria in semi-algebraic economies, which may be expressed as semi-algebraic systems. The approach is based on triangular decomposition and real solution classification, two powerful tools of algebraic computation. Its effectiveness is illustrated by two examples of application.Comment: 24 pages, 5 figure