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A Calculus for Exploiting Data Parallelism on Recursively Defined Data
 In Proc. International Workshop on Theory and Practice on Parallel Programming, LNCS
, 1994
"... Array based data parallel programming can be generalized in two ways to make it an appropriate paradigm for parallel processing of general recursively defined data. The first is the introduction of a parallel evaluation mechanism for dynamically allocated recursively defined data. It achieves the ef ..."
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Array based data parallel programming can be generalized in two ways to make it an appropriate paradigm for parallel processing of general recursively defined data. The first is the introduction of a parallel evaluation mechanism for dynamically allocated recursively defined data. It achieves the effect of applying the same function to all the subterms of a given datum in parallel. The second is a new notion of recursion, which we call parallel recursion, for parallel evaluation of recursively defined data. In contrast with ordinary recursion, which only uses the final results of the recursive calls of its immediate subterms, the new recursion repeatedly transforms a recursive datum represented by a system of equations to another recursive datum by applying the same function to each of the equation simultaneously, until the final result is obtained. This mechanism exploits more parallelism and achieves significant speedup compared to the conventional parallel evaluation of recursive ...
IR18410413A02 and U.S. Army grants DAA2984K0061, DAA298490027. Sublinear Parallel Time Recognition of Tree Adjoining ~anguages*
, 1988
"... A parallel algorithm is presented for recognizing the class of languages generated by tree adjoining grammars, a tree rewriting system which has applications in computational Linguistics. This class of languages is known to properly include all contextfree languages; for example, the noncontextfr ..."
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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 computational Linguistics. This class of languages is known to properly include all contextfree languages; for example, the noncontextfree sets {a " bncn} and {ww) are in this class. It is shown that the recognition problem for tree adjoining languages can be solved by a concurrentread, exclusivewrite parallel randomaccess machine (CREW PRAM) in 0 (log2(n)) time using polynomially many processors. This extends a previous result for contextfree languages.
Optimal Tree Ranking is in NC
"... This paper places the optimal tree ranking problem in NC. A ranking is a labeling of the nodes with natural numbers such that if nodes u and v have the same label then there exists another node with a greater label on the path between them. An optimal ranking is a ranking in which the largest label ..."
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This paper places the optimal tree ranking problem in NC. A ranking is a labeling of the nodes with natural numbers such that if nodes u and v have the same label then there exists another node with a greater label on the path between them. An optimal ranking is a ranking in which the largest label assigned to any node is as small as possible among all rankings. An O(n) sequential algorithm is known. Researchers have speculated that this problem is P complete. We show that for an nnode tree, one can compute an optimal ranking in O(log n) time using n 2 = log n CREW PRAM processors. In fact, our ranking is super critical in that the label assigned to each node is absolutely as small as possible. We achieve these results by showing that a more general problem, which we call the super critical numbering problem, is in NC. No NC algorithm for the super critical tree ranking problem, approximate or otherwise, was previously known; the only known NC algorithm for optimal tree ranking ...
Abstract Fast Parallel Recognition of LR Language Suffixes
"... It is shown that suffix recognition for deterministic contextfree languages can be done on a PRAM multiprocessor within the upper complexity bounds of the graph reachability problem. ..."
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It is shown that suffix recognition for deterministic contextfree languages can be done on a PRAM multiprocessor within the upper complexity bounds of the graph reachability problem.
Polynomial Time Algorithm Solving the Refutation Tree Problem for Formal Graph Systems
, 1993
"... The refutation tree problem is to compute a refutation tree which is associated with the structure of a graph generated by a formal graph system (FGS). We present subclasses of FGSs, called simple FGSs, sizebounded simple FGSs and bounded simple FGSs. In order to show that the refutation tree probl ..."
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The refutation tree problem is to compute a refutation tree which is associated with the structure of a graph generated by a formal graph system (FGS). We present subclasses of FGSs, called simple FGSs, sizebounded simple FGSs and bounded simple FGSs. In order to show that the refutation tree problem for simple FGSs can be solved in polynomial time, we prove that the refutation tree problem for sizebounded simple FGSs is NC 2 reducible to the graph ismorphism problem. For bounded simple FGSs, we show that the refutation tree problem is in NC 2 . We present an FGS 0 GI and show that the graph isomorphism problem is logspace reducible to the graph isomorphism problem for 0 GI . 1 Introduction A formal graph system (FGS) [21] is a kind of logic programs which deals with graphs just like terms [10]. By regarding terms as trees, conventional logic programs can be directly simulated by FGSs. Moreover, an elementary formal system [2, 3, 18], that is a logic program on strings, is als...