196 research outputs found
First Order Theories of Some Lattices of Open Sets
We show that the first order theory of the lattice of open sets in some
natural topological spaces is -equivalent to second order arithmetic. We
also show that for many natural computable metric spaces and computable domains
the first order theory of the lattice of effectively open sets is undecidable.
Moreover, for several important spaces (e.g., , , and the
domain ) this theory is -equivalent to first order arithmetic
Isomorphism versus commensurability for a class of finitely presented groups
We construct a class of finitely presented groups where the isomorphism problem is solvable but the commensurability problem is unsolvable. Conversely, we construct a class of finitely presented groups within which the commensurability problem is solvable but the isomorphism problem is unsolvable. These are first examples of such a contrastive complexity behaviour with respect to the isomorphism problem
Lambda theories of effective lambda models
A longstanding open problem is whether there exists a non-syntactical model
of untyped lambda-calculus whose theory is exactly the least equational
lambda-theory (=Lb). In this paper we make use of the Visser topology for
investigating the more general question of whether the equational (resp. order)
theory of a non syntactical model M, say Eq(M) (resp. Ord(M)) can be
recursively enumerable (= r.e. below). We conjecture that no such model exists
and prove the conjecture for several large classes of models. In particular we
introduce a notion of effective lambda-model and show that for all effective
models M, Eq(M) is different from Lb, and Ord(M) is not r.e. If moreover M
belongs to the stable or strongly stable semantics, then Eq(M) is not r.e.
Concerning Scott's continuous semantics we explore the class of (all) graph
models, show that it satisfies Lowenheim Skolem theorem, that there exists a
minimum order/equational graph theory, and that both are the order/equ theories
of an effective graph model. We deduce that no graph model can have an r.e.
order theory, and also show that for some large subclasses, the same is true
for Eq(M).Comment: 15 pages, accepted CSL'0
Fuzzy Automata: A Quantitative Review
Classical automata theory cannot deal with the system uncertainty. To deal with the system uncertainty the concept of fuzzy finite automata was proposed. Fuzzy automata can be used in diverse applications such as fault detection, pattern matching, measuring the fuzziness between strings, description of natural languages, neural network, lexical analysis, image processing, scheduling problem and many more. In this paper, a methodical literature review is carried out on various research works in the field of Fuzzy automata and explained the challenging issues in the field of fuzzy automata
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