In this note we characterize all subalgebras and homomorphic images of the free cyclic Heyting algebra, also known as the RiegerNishimura lattice N . Consequently, we prove that every subalgebra of N is projective, that a finite Heyting algebra is a subalgebra of N iff it is projective, and characterize projective homomorphic images of N . The atoms and co-atoms of the lattice of all subalgebra...

The main result of this paper is the decidability of the membership problem for 2 × 2 nonsingular integer matrices. Namely, we will construct the first algorithm that for any nonsingular 2 × 2 integer matrices M1, . . . ,Mn and M decides whether M belongs to the semigroup generated by {M1, . . . ,Mn}. Our algorithm relies on a translation of numerical problems on matrices into combinatorial pro...

In this paper we introduce the simultaneous membership problem, defined for any graph class C characterized in terms of representations, e.g. any class of intersection graphs. Two graphs G1 and G2, sharing some vertices X (and the corresponding induced edges), are said to be simultaneous members of graph class C, if there exist representations R1 and R2 of G1 and G2 that are “consistent” on X ....

This article presents an overview of a framework called categorial grammars from a theoretical and algorithmic perspective. It provides an introduction to the formalisms of these grammars and of the tools they use (the Lambek Calculus) for theoretical computer scientists who are not familiar with them. We give a clear presentation of the main classical and recent results on these grammars, espe...

Consider a group of nodes connected through multiple-access channels and the only observable feedback on the channel is a binary value: either one or more nodes have transmitted (busy), or no node has transmitted (idle). The channel model thus described is called Beeping Model and captures computation in hardware using a group of sequential circuit modules connected by a logic-OR gate. It has a...

Throughout, P is the semigroup presentation 〈a, b: bab = ab〉 for the semigroup S1. Lallement and Rosaz, [5], have shown that the semigroups Sk having presentations 〈a, b: b(ab)b = ab〉 are residually finite. They also find normal forms for elements of Sk . Specialized to k = 1, every element of S1 is either a power of a or else it can be represented uniquely by a word in one of the forms aba or ...

Consider a group of nodes connected through multiple-access channels and the only observable feedback on the channel is a binary value: either one or more nodes have transmitted (busy), or no node has transmitted (idle). The channel model thus described is called Beeping Model and captures computation in hardware using a group of sequential circuit modules connected by a logic-OR gate. It has a...

There exists a feasible procedure to decide whether or not an arbitrary polynomial belongs to a given ideal in Z[x] if the ideal’s minimal basis is known. However, when this is not the case there is no feasible procedure to decide whether or not an arbitrary polynomial belongs to a given ideal. There already exists an effective procedure to find an ideal’s minimal basis, but it depends on solvi...

The purpose of this paper is establish the usefulness of newly formed modified s-curve membership function in a limited supply production planning problem with continuous variables. In this respect fuzzy parameters of linear programming are modeled by non-linear membership function such as scurve function. This paper begins with introduction and construction of modified s-curve membership funct...