An Improved Tight Closure Algorithm for Integer Octagonal Constraints

Integer octagonal constraints (a.k.a. ``Unit Two Variables Per Inequality'' or ``UTVPI integer constraints'') constitute an interesting class of constraints for the representation and solution of integer problems in the fields of constraint programming and formal analysis and verification of software and hardware systems, since they couple algorithms having polynomial complexity with a relatively good expressive power. The main algorithms required for the manipulation of such constraints are the satisfiability check and the computation of the inferential closure of a set of constraints. The latter is called `tight' closure to mark the difference with the (incomplete) closure algorithm that does not exploit the integrality of the variables. In this paper we present and fully justify an O(n^3) algorithm to compute the tight closure of a set of UTVPI integer constraints.Comment: 15 pages, 2 figure

Testing a system specified using Statecharts and Z

A hybrid specification language SZ, in which the dynamic behaviour of a system is described using Statecharts and the data and the data transformations are described using Z, has been developed for the specification of embedded systems. This paper describes an approach to testing from a deterministic sequential specification written in SZ. By considering the Z specifications of the operations, the extended finite state machine (EFSM) defined by the Statechart can be rewritten to produce an EFSM that has a number of properties that simplify test generation. Test generation algorithms are introduced and applied to an example. While this paper considers SZ specifications, the approaches described might be applied whenever the specification is an EFSM whose states and transitions are specified using a language similar to Z

Including non-functional issues in Anna/Ada programs for automatic implementation selection

We present an enrichment of the Anna specification language for Ada aimed at dealing not only with functional specification of packages but also with non-functional information about them. By non-functional information we mean information about efficiency, reliability and, in general, any software attribute measuring somehow the quality of software (perhaps in a subjective manner). We divide this information into three kinds: definition of non-functional properties, statement of non-functional behaviour and statement of non-functional requirements; like Anna annotations, all of this information appears in Ada packages and package bodies and their syntax is close to Ada constructs. Non-functional information may be considered not only as valuable comments, but also as an input for an algorithm capable of selecting the “best” package body for every package definition in a program, the “best” meaning the one that fits the set of non-functional requirements of the package in the program.Peer ReviewedPostprint (author's final draft

The Parma Polyhedra Library: Toward a Complete Set of Numerical Abstractions for the Analysis and Verification of Hardware and Software Systems

Since its inception as a student project in 2001, initially just for the handling (as the name implies) of convex polyhedra, the Parma Polyhedra Library has been continuously improved and extended by joining scrupulous research on the theoretical foundations of (possibly non-convex) numerical abstractions to a total adherence to the best available practices in software development. Even though it is still not fully mature and functionally complete, the Parma Polyhedra Library already offers a combination of functionality, reliability, usability and performance that is not matched by similar, freely available libraries. In this paper, we present the main features of the current version of the library, emphasizing those that distinguish it from other similar libraries and those that are important for applications in the field of analysis and verification of hardware and software systems.Comment: 38 pages, 2 figures, 3 listings, 3 table