We study a class of inverse monoids of the form M = Inv〈X |w = 1〉, where the single relator w has a combinatorial property that we call sparse. For a sparse word w, we prove that the word problem for M is decidable. We also show that the set of words in (X ∪X) that represent the identity in M is a deterministic context free language, and that the set of geodesics in the Schützenberger graph of ...

This report extends the scope of computation with a non standard × to the more basic case of a non standard +, where standard means associative and commutative. Two physically meaningful examples of a nonstandard + are provided by the observation of motion in Special Relativity, from either outside (3D) or inside (2D or more), We revisit the “gyro”-theory of Ungar to present the polymorphic inf...

The word problem for confluent Thue systems is linear-time and for almost confluent systems it is PSPACE-complete. Here we consider a single length-preserving rule, of the form xy ↔ yx, whose word problem could turn out to be tractable. A search for normal forms leads to the conjecture that if xy ↔ xy then m = p and n = q. We prove a stronger version of this: in a group G with the single relato...

| In this paper we consider a CDMA system with error control coding. Optimal joint decoding is prohibitively complex. Instead we propose a sequential approach for handling the multiple access interference and the error control decoding. The error control decoding is implemented via single user soft{input decoders utilising metrics generated by linear algebraic multiuser metric generators. The d...

By working out an appropriate technique of relations and relators and extending the ideas of the direct methods of Z. Gajda and R. Ger, we prove some generalizations of the stability theorems of D. H. Hyers, T. Aoki, Th. M. Rassias and P. Gavruţǎ in terms of the existence and unicity of 2–homogeneous and additive approximate selections of generalized subadditive relations of semigroups to vecto...