Abstract
The algebraic theory we present here continues the early work of Chomsky-Schützenberger [Ch,Sch], Shamir [Sh] and Nivat [N]. The leading idea is to develop a machine and production free language theory. The interest in such a theory is support by the hope that the proofs in such a theory don't need so much case discussions which often lead to errors and that a view which is free from non-essentials of language theory will lead to a progress in the direction of our problems. Even if the theory is in an early stage the attempt pays out in a machine free definition of LL(k) and LR(k) languages which leads easily to generalisations of non-deterministic LL(k) and LR(k) languages with the same space and time complexity behaviour. Too, we are able to show that this theory is not restricted to the context free languages but also concerns the whole Chomsky hierarchy. Our theory is in a sense a dual to the theory of formal power series as introduced by M. Schützenberger.
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Hotz, G. (1984). Outline of an algebraic language theory. In: Chytil, M.P., Koubek, V. (eds) Mathematical Foundations of Computer Science 1984. MFCS 1984. Lecture Notes in Computer Science, vol 176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030290
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DOI: https://doi.org/10.1007/BFb0030290
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