Clemens Lautemann

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We start with some definitions about probabilistic Turing machines (for a detailed exposition of this subject the reader is referred to [2]). Our basic model of computation is the Turing machine with input alphabet S z (0, l}. All machines are assumed to have two terminal states, namely q0 (reject) and 9, (accept). A probabilistic Turing machine (PTM) is(More)
A language L over an alphabet A is said to have a neutral letter if there is a letter e ∈ A such that inserting or deleting e’s from any word in A∗ does not change its membership or non-membership in L. The presence of a neutral letter affects the definability of a language in firstorder logic. It was conjectured that it renders all numerical predicates(More)
Although in many ways, hyperedge replacement graph grammars (HRGs) are, among all graph generating mechanisms, what context-free Chomsky grammars are in the realm of string rewriting, their parsing problem is known to be, in general, NP-complete. In this paper, the main difficulty in HRG parsing is analysed and some conditions on either grammar or input(More)
In this paper we prove that the class of functions expressible by first order formulas with only two variables coincides with the class of functions computable by AC<sup>0</sup> circuits with a linear number of gates. We then investigate the feasibility of using Ehrenfeucht-Fraisse games to prove lower bounds for that class of circuits, as well as for(More)
The counting ability of weak formalisms is of interest as a measure of their expressive power. The question was investigated in several papers in complexity theory [ABO84,FKPS85,DGS86] and in weak arithmetic [PW87]. In each case, the considered formalism (AC0{circuits, rst{order logic, 0, respectively) was shown to be able to count precisely up to a(More)