Turku Centre for Computer Science

About: Turku Centre for Computer Science is a facility organization based out in Turku, Finland. It is known for research contribution in the topics: Decidability & Word (group theory). The organization has 382 authors who have published 1027 publications receiving 19560 citations.

Compositions over a finite domain: from completeness to synchronizable automata

Abstract: We will consider functions whose domain is a fixed finite set N with n elements, n ≥ 2, and whose range is included in N. Such a setup occurs in many and very diverse situations. Depending on the interpretation, different questions will be asked. The two interpretations we have had mostly in mind are many-valued logic and finite deterministic automata. In the former, the set N consists of n truth values, and the functions are truth functions. In the latter, the set N consists of the states of an automaton, whereas each letter of the input alphabet induces a specific function: the next state when reading that letter. We will consider two specific issues concerning functions of the kind mentioned: completeness and complexity of compositions. While the former is fairly well understood, very little is known about the latter. Our starting point is an old conjecture, falling within the framework of the complexity of computations, concerning finite deterministic automata. Variants and generalizations of this conjecture are presented. It is also shown that the conjecture does not hold for functions of several variables

A correlation ratio for possibility distributions

Abstract: Generalizing the probabilistic correlation ratio we will introduce a correlation ratio for marginal possibility distributions of joint possibility distributions.

Implementation Issues Concerning the Action Systems Formalism

Abstract: Formal methods have emerged as a rigorous framework for developing correct parallel and distributed software. However, implementation of these systems is often difficult to realize. This paper proposes a number of practical solutions to problems regarding implementation of parallel programs developed using formal methods. We focus on implementation using industry standard software and hardware. We propose a new approach to combine partitioning, scheduling and rollback into a convenient solution for implementing parallel systems. A proof-of-concept tool, ELSA, has been developed hand in hand with our research to demonstrate the applicability of our methods. We also provide a theoretical foundation as justification for our methods.

The most general conservation law for a cellular automaton

Abstract: We study the group-valued and semigroup-valued conservation laws in cellular automata (CA). We provide examples to distinguish between semigroup-valued, group-valued and real-valued conservation laws. We prove that, even in one-dimensional case, it is undecidable if a CA has any non-trivial conservation law of each type. For a fixed range, each CA has a most general (group-valued or semigroup-valued) conservation law, encapsulating all conservation laws of that range. For one-dimensional CA the semigroup corresponding to such a most general conservation law has an effectively constructible finite presentation, while for higher-dimensional ones no such effective construction exists.