Uniform decision problems in automatic semigroups

We consider various decision problems for automatic semigroups, which involve the provision of an automatic structure as part of the problem instance. With mild restrictions on the automatic structure, which seem to be necessary to make the problem well-defined, the uniform word problem for semigroups described by automatic structures is decidable. Under the same conditions, we show that one can also decide whether the semigroup is completely simple or completely zero-simple; in the case that it is, one can compute a Rees matrix representation for the semigroup, in the form of a Rees matrix together with an automatic structure for its maximal subgroup. On the other hand, we show that it is undecidable in general whether a given element of a given automatic monoid has a right inverse.Comment: 19 page

Some undecidability results concerning the property of preserving regularity

AbstractA finite string-rewriting system R preserves regularity if and only if it preserves Σ-regularity, where Σ is the alphabet containing exactly those letters that have occurrences in the rules of R. This proves a conjecture of Gyenizse and Vágvölgyi (1997). In addition, some undecidability results are presented that generalize results of Gilleron and Tison (1995) from term-rewriting systems to string-rewriting systems. It follows that the property of being regularity preserving is undecidable for term-rewriting systems, thus answering another question of Gyenizse and Vágvölgyi (1997). Finally, it is shown that it is undecidable in general whether a finite, lengthreducing, and confluent string-rewriting system yields a regular set of normal forms for each regular language

Die Korb-Bienenzucht : eine kurze und deutliche Anweisung, die Bienen in Strohkörben naturgemäß und vortheilhaft zu behandeln, alle Arten von Strohstöcken sowol für ein Volk, als auch für mehr Völker, mit ganz besonderer Berücksichtigung der ....

Achtung. Seite 17 fehlt (beim Scannen übersehen)!!! Vollst. Titel: Die Korb-Bienenzucht : eine kurze und deutliche Anweisung, die Bienen in Strohkörben naturgemäß und vortheilhaft zu behandeln, alle Arten von Strohstöcken sowol für ein Volk, als auch für mehr Völker, mit ganz besonderer Berücksichtigung der Dzierzonschen Methode, anzufertigen und die Bienenkolonien auf einfache, fast kunstlose und doch sichere Weise mit Erfolg zu vermehren ; nebst kurzen Andeutungen der Beschäftigungen des Bienenzüchters in jedem Monat des Jahres / bearb. und hrsg. von Friedrich Otto Roth

Reduction relations for monoid semirings

AbstractIn this paper we study rewriting techniques for monoid semirings. Based on disjoint and non-disjoint representations of the elements of monoid semirings we define two different reduction relations. We prove that in both cases the reduction relation describes the congruence that is induced by the underlying set of equations, and we study the termination and confluence properties of the reduction relations

On determinism versus nondeterminism for restarting automata

AbstractA restarting automaton processes a given word by executing a sequence of local simplifications until a simple word is obtained that the automaton then accepts. Such a computation is expressed as a sequence of cycles. A nondeterministic restarting automaton M is called correctness preserving, if, for each cycle u⊢Mcv, the string v belongs to the characteristic language LC(M) of M, if the string u does. Our first result states that for each type of restarting automaton X∈{R,RW,RWW,RL,RLW,RLWW}, if M is a nondeterministic X-automaton that is correctness preserving, then there exists a deterministic X-automaton M1 such that the characteristic languages LC(M1) and LC(M) coincide. When a restarting automaton M executes a cycle that transforms a string from the language LC(M) into a string not belonging to LC(M), then this can be interpreted as an error of M. By counting the number of cycles it may take M to detect this error, we obtain a measure for the influence that errors have on computations. Accordingly, this measure is called error detection distance. It turns out, however, that an X-automaton with bounded error detection distance is equivalent to a correctness preserving X-automaton, and therewith to a deterministic X-automaton. This means that nondeterminism increases the expressive power of X-automata only in combination with an unbounded error detection distance

A typology of church attitudes towards the state with special reference to the German church controversy, 1933-1945.

Thesis (Ph.D.)--Boston UniversityThe purpose of this investigation is to trace the development of the various attitudes of the church towards the state and to establish some definite attitudinal types with special reference to the church controversy in Germany from 1933 - 1945. On account of the complexity of the subject, the study makes use of three disciplines: theology, history of religion and sociology of religion. The church controversy in Germany will enter the history of the universal church as a twentieth century revelation of the original problem of the attitude of the Christian Church towards the state. The attitudes of opposition, accommodation, co-ordination and identification express each in its own way the desire to find a solution to the perplexing problem of the relationship of the two institutions. [TRUNCATED