Abstract
It is known, that over 1-dimensional strings, the expressive power of 2-way multihead (non) deterministic automata and (non) deterministic Transitive Closure formulas is (non) deterministic log space [Ib73, Im88]. However, the subset of formulas needed to simulate exactly k heads is unknown. It is also unknown if the automata and formulas have the same expressive power over more general structures such as multidimensional grids. We define a reduction from k-head automata to formulas of arity k, which works also for grids. The method used is a generalization of [K156], and the formulas obtained are a generalization of regular expressions to multihead automata and to grid languages. As simple applications, we use the reduction to show that the power of formulas of arity 1 over strings define (classical) regular languages, to give a simpler equivalent of the L=NL open problem, and to establish the equivalence of the automata and formulas over grids.
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© 1992 Springer-Verlag Berlin Heidelberg
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Bargury, Y., Makowsky, J. (1992). The expressive power of transitive closure and 2-way multihead automata. In: Börger, E., Jäger, G., Kleine Büning, H., Richter, M.M. (eds) Computer Science Logic. CSL 1991. Lecture Notes in Computer Science, vol 626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023754
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DOI: https://doi.org/10.1007/BFb0023754
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