Implicit Real Vector Automata

peer reviewedThis paper addresses the symbolic representation of non-convex real polyhedra, i.e., sets of real vectors satisfying arbitrary Boolean combinations of linear constraints. We develop an original data structure for representing such sets, based on an implicit and concise encoding of a known structure, the Real Vector Automaton. The resulting formalism provides a canonical representation of polyhedra, is closed under Boolean operators, and admits an efficient decision procedure for testing the membership of a vector

The earlier the better: a theory of timed actor interfaces

Programming embedded and cyber-physical systems requires attention not only to functional behavior and correctness, but also to non-functional aspects and specifically timing and performance constraints. A structured, compositional, model-based approach based on stepwise refinement and abstraction techniques can support the development process, increase its quality and reduce development time through automation of synthesis, analysis or verification. For this purpose, we introduce in this paper a general theory of timed actor interfaces. Our theory supports a notion of refinement that is based on the principle of worst-case design that permeates the world of performance-critical systems. This is in contrast with the classical behavioral and functional refinements based on restricting or enlarging sets of behaviors. An important feature of our refinement is that it allows time-deterministic abstractions to be made of time-non-deterministic systems, improving efficiency and reducing complexity of formal analysis. We also show how our theory relates to, and can be used to reconcile a number of existing time and performance models and how their established theories can be exploited to represent and analyze interface specifications and refinement steps.\u

Real-Time Vector Automata

We study the computational power of real-time finite automata that have been augmented with a vector of dimension k, and programmed to multiply this vector at each step by an appropriately selected $k \times k$ matrix. Only one entry of the vector can be tested for equality to 1 at any time. Classes of languages recognized by deterministic, nondeterministic, and "blind" versions of these machines are studied and compared with each other, and the associated classes for multicounter automata, automata with multiplication, and generalized finite automata.Comment: 14 page

Dynamic systems as tools for analysing human judgement

With the advent of computers in the experimental labs, dynamic systems have become a new tool for research on problem solving and decision making. A short review on this research is given and the main features of these systems (connectivity and dynamics) are illustrated. To allow systematic approaches to the influential variables in this area, two formal frameworks (linear structural equations and finite state automata) are presented. Besides the formal background, it is shown how the task demands of system identification and system control can be realized in these environments and how psychometrically acceptable dependent variables can be derived

The earlier the better: a theory of timed actor interfaces

Programming embedded and cyber-physical systems requires attention not only to functional behavior and correctness, but also to non-functional aspects and specifically timing and performance. A structured, compositional, model-based approach based on stepwise refinement and abstraction techniques can support the development process, increase its quality and reduce development time through automation of synthesis, analysis or verification. Toward this, we introduce a theory of timed actors whose notion of refinement is based on the principle of worst-case design that permeates the world of performance-critical systems. This is in contrast with the classical behavioral and functional refinements based on restricting sets of behaviors. Our refinement allows time-deterministic abstractions to be made of time-non-deterministic systems, improving efficiency and reducing complexity of formal analysis. We show how our theory relates to, and can be used to reconcile existing time and performance models and their established theories

Representing a P-complete problem by small trellis automata

A restricted case of the Circuit Value Problem known as the Sequential NOR Circuit Value Problem was recently used to obtain very succinct examples of conjunctive grammars, Boolean grammars and language equations representing P-complete languages (Okhotin, http://dx.doi.org/10.1007/978-3-540-74593-8_23 "A simple P-complete problem and its representations by language equations", MCU 2007). In this paper, a new encoding of the same problem is proposed, and a trellis automaton (one-way real-time cellular automaton) with 11 states solving this problem is constructed