By Amir M. Ben-Amram (auth.), Torben Æ. Mogensen, David A. Schmidt, I. Hal Sudborough (eds.)

By offering state of the art points of the idea of computation, this publication commemorates the sixtieth birthday of Neil D. Jones, whose medical occupation parallels the evolution of computation idea itself.
The 20 reviewed examine papers awarded including a quick survey of the paintings of Neil D. Jones have been written by way of scientists who've labored with him, within the roles of scholar, colleague, and, in a single case, mentor. according to the Festschrift's subtitle, the papers are geared up in elements on computational complexity, application research, and software transformation.

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This supports Conjecture 1. On the other hand, we will see that if functions of several variables are considered, then the statement analogous to Conjecture 1 is not valid. The variant of Conjecture 1, dealing with the depths of individual functions, can be expressed as follows. Conjecture 2 If ci is a constant, then D (ci ) = n(n − 1). It is a consequence of Theorem 1 that the depth n(n − 1) cannot be reduced. If Conjecure 1 holds, so does Conjecture 2. This is a consequence of the following simple result.

We can also view constants as targets and search for the shortest composition sequence for a target. The above general framework can be applied also to the truth-functions of many-valued logic, [13,14]. Many combinatorial problems fall also within the same framework. In the road coloring problem one is given a finite directed graph G, where the edges are unlabeled. The task is to find a labeling of the edges that turns G into a deterministic automaton possessing a synchronizing word, [1]. ) The term ”road coloring” is due to the following interpretation.

Properties of n such as primality or being a power of 2 turn out to be important, independently of the semantic interpretation. Most of the questions about depth, as well as about the comparison of different notions of depth, remain open. Our results show that the study of functions of several variables may shed light also to the case where all functions considered are unary. 1 Introduction We will consider an old unsolved problem about finite deterministic automata in a more general setup. The generalization shows the close interconnection of the original problem with issues in many-valued logic, graph theory and combinatorics.

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