Abstract
We present a new lower bound argument for oblivious parity-branching programs which allows to prove exponential lower bounds on the width if the length is restricted to be linear or at most o(n · log(n)). This solves an open problem because "Cut & Paste" arguments which provided bounds of the same quality in the case of determinism, nondeterminism, and co-nondeterminism [AM86] [KMW89] do not work in the case of parity-acceptation. Our technique is applicable to some well-known decision problems such as the graph-accessibility-problem of directed graphs, and the word problems of free groups of finite rank. Using well-known results on the simulation of logspace-bounded Turing machines by sequences of branching programs we give at least the complete separation of the complexity classes L, NL, co-NL, ⊕L, and AL=P for oblivious Turing machines of linear access time.
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Krause, M. (1990). Separating ⊕L from L, NL, co-NL and AL (=P) for Oblivious turing machines of linear access time. In: Rovan, B. (eds) Mathematical Foundations of Computer Science 1990. MFCS 1990. Lecture Notes in Computer Science, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029633
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DOI: https://doi.org/10.1007/BFb0029633
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