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Displaying 121 –
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518
Motivated by the wavelength division multiplexing in all-optical networks, we consider the problem of finding an optimal (with respect to the least possible number of wavelengths) set of internally node disjoint dipaths connecting all pairs of distinct nodes in the binary -dimensional hypercube, where . This system of dipaths constitutes a routing protocol that remains functional in the presence of up to faults (of nodes and/or links). The problem of constructing such protocols for general...
Four notions of factorizability over arbitrary directed graphs are examined. For acyclic graphs they coincide and are identical with the usual factorization of probability distributions in Markov models. Relations between the factorizations over circuits are described in detail including nontrivial counterexamples. Restrictions on the cardinality of state spaces cause that a factorizability with respect to some special cyclic graphs implies the factorizability with respect to their, more simple,...
Temporal Constraint Networks are a well-defined, natural and efficient formalism for representing temporal knowledge based on metric temporal constraints. They support the representation of both metric and some qualitative temporal relations and are provided with efficient algorithms based on CSP techniques. Recently, a generalization based on fuzzy sets has been proposed in order to cope with vagueness in temporal relations. In this paper we generalize some earlier definitions for Fuzzy Temporal...
We investigate a Gentzen-style proof system for the first-order -calculus based on cyclic proofs, produced by unfolding fixed point formulas and detecting repeated proof goals. Our system uses explicit ordinal variables and approximations to support a simple semantic induction discharge condition which ensures the well-foundedness of inductive reasoning. As the main result of this paper we propose a new syntactic discharge condition based on traces and establish its equivalence with the semantic...
We investigate a Gentzen-style proof system for the first-order μ-calculus
based on cyclic proofs, produced by unfolding fixed point formulas
and detecting repeated proof goals. Our system uses explicit ordinal
variables and approximations to support a simple semantic induction
discharge condition which ensures the well-foundedness of inductive
reasoning. As the main result of this paper we propose a new syntactic
discharge condition based on traces and establish its equivalence
with the semantic...
The graph product is an operator mixing direct and free products. It is already known that free products and direct products of automatic monoids are automatic. The main aim of this paper is to prove that graph products of automatic monoids of finite geometric type are still automatic. A similar result for prefix-automatic monoids is established.
The graph product is an operator mixing direct and free products. It is already known that free
products and direct products of automatic monoids are automatic. The main aim of this paper is to
prove that graph products of automatic monoids of finite geometric type are still automatic.
A similar result for prefix-automatic monoids is established.
We have been investigating the cryptographical properties of
in nite families of simple graphs of large girth with the special colouring
of vertices during the last 10 years. Such families can be used for the
development of cryptographical algorithms (on symmetric or public key
modes) and turbocodes in error correction theory. Only few families of
simple graphs of large unbounded girth and arbitrarily large degree are
known.
The paper is devoted to the more general theory of directed graphs of
large...
A well-known theorem of Rabin yields a dimensional lower bound on the width of complete polynomial proofs of a system of linear algebraic inequalities. In this note we investigate a practically motivated class of systems where the same lower bound can be obtained on the width of almost all (noncomplete) linear proofs. The proof of our result is based on the Helly Theorem.
Positioned eco-grammar systems (PEG systems, for short) were introduced in our previous papers. In this paper we engage in a new field of research, the hierarchy of PEG systems, namely in the hierarchy of the PEG systems according to the number of agents presented in the environment and according to the number of types of agents in the system.
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