A parallel algorithm is presented for recognizing the class of languages generated by tree adjoining grammars, a tree rewriting system which has applications in natural language processing. This class of languages is ...
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A parallel algorithm is presented for recognizing the class of languages generated by tree adjoining grammars, a tree rewriting system which has applications in natural language processing. This class of languages is known to properly include all context-free languages;for example, the noncontext-free sets {a(n)b(n)c(n)} and {ww} are in this class. It is shown that the recognition problem for tree adjoining languages can be solved by a concurrent read, concurrent write parallel random-access machine (CRCW PRAM) in O(log n) time using polynomially many processors. Thus, the class of tree adjoining languages is in AL1 and hence in NL. This extends a previous result for context-free languages.
In this work we address the parallelcomplexity of two combinatorial problems, specifically the problems of the existence and of the construction of a parity base of preassigned weight ( exact parity base for short) i...
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In this work we address the parallelcomplexity of two combinatorial problems, specifically the problems of the existence and of the construction of a parity base of preassigned weight ( exact parity base for short) in a 0-1 weighted, represented matroid, subject to parity conditions. We prove that these problems lie in the parallelcomplexity class RNC 2 , i.e. they are solvable with one-sided error by a logspace uniform family of bounded fan-in circuits of polynomial size and quadratic logarithmic depth which receive, in addition to the problem input, a polynomial number of random input bits. We also show that the more general cases of these problems, defined over matroids weighted with integral instead of 0-1 weights, also belong to RNC 2 , as long as the weights are given in unary notation. As a consequence some special cases of these problems, which are of independent interest, belong to the same parallelcomplexity class: examples of these are the problem of the construction of a perfect matching of preassigned weight in a 0-1 weighted graph, recently addressed in [1], or that of the construction of a base of preassigned weight, in the intersection of two 0-1 weighted represented matroids.
It is shown for rationale a,b≥1a,b≥1a, b \geq 1 that <span class="MathJax" id="MathJax-Element-4-Frame" tabindex="0" style="position: relative;" data-mathml='<ma...
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