SOME GROUP THEORETIC ASPECTS OF t-NORMS

Some Group Theoretic Aspects of t-Norms

Let A be the automorphism group of the unit interval with its usual order relation, and let B be the embedding of the multiplicative group of positive real numbers into A given by exponentiation. Strict t-norms are in one-to-one correspondence with the right cosets of B in A: Here, we identify the normalizer N of B in A and give explicit formulas for the corresponding set of t-norms.

Random Permutations: Some Group-Theoretic Aspects

The study of asymptotics of random permutations was initiated by Erdos and Tunto. in a series of papers from 1965 to 1968, and has been much studied since. Recent developments in permutation group theory make it reasonable to ask questions with a more grouptheoretic flavour. Two examples considered here are membership in a proper transitive subgroup, and the intersection of a subgroup with a ra...

Some graph theoretic aspects of finite geometries

Some Experimental Aspects of Optimality-Theoretic Pragmatics

The article has three main concerns: (i) it gives a concise introduction into optimality-theoretic pragmatics; (ii) it discusses the relation to alternative accounts (relevance theory and Levinson's theory of presumptive meanings); (iii) it reviews recent findings concerning the psychological reality of optimality-theoretic pragmatics and its central part concept – bidirectional optimization. A...

Complexity Theoretic Aspects of Some Cryptographic Functions

In this work, we are interested in non-trivial upper bounds on the spectral norm of binary matrices M from {−1, 1} . It is known that the distributed Boolean function represented by M is hard to compute in various restricted models of computation if the spectral norm is bounded from above by N, where ε > 0 denotes a fixed constant. For instance, the size of a two-layer threshold circuit (with p...