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Leistungen
The objective of the project was to update computer science facilities for the NIS participants and launch joint research based on the current research activities. Under the support or partial support of the project the participants solved some problems concerning theoretical and applied aspects of logic and algebra. In particular, formalisms for dynamic logics of proofs and for some type of discrete dynamic systems were developed. The complexity issues concerning the latter systems as well as linear logics and their applications to Petri nets were investigated. Equational characterisations of solid pseudovarieties using both identities and pseudoidentities were found. The initial phase of cooperation has permitted precise further directions of joint research to be made which are planned to be extended towards model-checking for programs acting under explicit time constraints and on their safety.
The received results are theoretical. E.Dantsin (POMI) has found a precise formalisation of interactive proof systems which were intensively studied last year and can be applied to self-checking programs and fast verification of proof correctness. S. Artemov (SMI) introduced and studied the Dynamic Logic of Proofs as a labeled modal logic describing abstract proporitional operations over proofs. The corresponding systems of axioms are proved to be decidable and complete with respect to the intended arithmetical interpretation. M. Volkov (USU) and his colleagues have given equational characterisations of solid pseudovarieties using both identities and pseudoidentities, in particular they showed that all solid pseudovarieties of semigroups are equational, that is, are exactiy finite parts of solid semigroup varieties. M. Kanovich (RSUH) continued his research on linear logic representations of different computation tools such as Horn programs Petri nets and vector games. This permits the introduction of new semantics for Linear Logic and the clarification of many results on the complexity of natural fragments of Linear Logic. A.Dikovsky and M.Dekhtyar (KIAM) presented several properties of discrete dynamic systems and formulate them in terms of logic programs with updates over finite databases with integrity constraints.
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