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This paper presents a survey of recent results in the theory of rational sets in arbitrary monoids. Main topics considered here are : the so-called Kleene monoids (i.e. monoids where Kleene's theorem holds), rational functions and relations, rational sets in partially commutative monoids, and rational sets in free groups.
The theory of algebraic abstract types specified by conditional equations is extended to types with “nonstrict” operations, partial and even infinite objects based on the concept of partial interpretations. Models of such types are studied where all explicit equations have solutions. Higher order types, i.e. types comprising higher order functions are treated, too. This allows an algebraic (“equational”)...
We study languages which can be described as limits of fast converging infinite sequences of context-free languages. Such a sequence $$L_0 \subseteq L_1 \subseteq L_2 \subseteq$$ ... is fast converging if each string w of its limit language belongs to an Li which has a grammatical description very concise in comparison with the length of w . We prove that these languages are closely related...
The concept for modules in software engineering based on equational algebraic specifications is extended by a suitable notion of constraints. This allows to have loose specifications with constraints for parameter, export and import interfaces of module specifications without loosing executability of the body specification. Correctness of such module specifications ensures that data types satisfying...
We have presented the outlines of a system which integrates three rather distinct modern technologies for intelligent systems which share the property of having a relational model, but which otherwise have very little in common. Due to lack of space I cannot include a convincing example which will show that the RL language will be a convenient tool for expressing real life rules, but my experience...
The FGCS project in Japan did not select Lisp as a kernel language, but a logic programming language like Prolog because of its powerful functions based on unification and its high productivity. The logic programming language itself is based on theorem proving such as SLD resolution. Studies of theorem proving or proof checking play an essential role in the total plans of FGCS in Japan. Computer science...
In this paper we discuss a collection of geometric location problems in the plane and their associated time complexity. These problems can be formulated as optimization problems. However, geometric properties are exploited to obtain efficient solutions. Among the problems considered are minimum enclosing circle, largest empty circle, fixed circle placement, and their variations. Most of the algorithms...
We present a new, and basically simple, algorithm for maintaining a structure supporting insert, delete and search in O(log2n) with no storage requirements other than that of the data itself.
We describe a deterministic simulation of PRAMs on module parallel computers (MPCs) and on processor networks of bounded degree. The simulating machines have the same number n of processors as the simulated PRAM, and if the size of the PRAM's shared memory is polynomial in n, each PRAM step is simulated by O(log n) MPC steps or by O((log n)2) steps of the bounded degree network. This improves upon...
We consider the design of two well-known optimal time adders: the ”carry look-ahead” adder ([BrKu]) and the ”conditional sum” adder ([Sk]). It is shown, that 6log(n) – 4, resp. 6log(n)+2, test patterns suffice to exhaustively test the n-bit carry look-ahead adder, resp. the n-bit conditional sum adder with respect to the single stuck-at fault model.
The computation of Boolean functions by parallel computers with shared memory (PRAMs and WRAMs) is considered. In particular complexity measures for parallel computers like critical and sensitive complexity are compared with other complexity measures for Boolean functions like branching program depth and length of prime implicants and clauses. The relations between these complexity measures and their...
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