Topic
LOGCFL
About: LOGCFL is a research topic. Over the lifetime, 84 publications have been published within this topic receiving 3253 citations.
Papers published on a yearly basis
Papers
TL;DR: An attempt is made to identify important subclasses of NC and give interesting examples in each subclass, and a new problem complete for deterministic polynomial time is given, namely, finding the lexicographically first maximal clique in a graph.
Abstract: The class NC consists of problems solvable very fast (in time polynomial in log n ) in parallel with a feasible (polynomial) number of processors. Many natural problems in NC are known; in this paper an attempt is made to identify important subclasses of NC and give interesting examples in each subclass. The notion of NC 1 -reducibility is introduced and used throughout (problem R is NC 1 -reducible to problem S if R can be solved with uniform log-depth circuits using oracles for S ). Problems complete with respect to this reducibility are given for many of the subclasses of NC . A general technique, the “parallel greedy algorithm,” is identified and used to show that finding a minimum spanning forest of a graph is reducible to the graph accessibility problem and hence is in NC 2 (solvable by uniform Boolean circuits of depth O (log 2 n ) and polynomial size). The class LOGCFL is given a new characterization in terms of circuit families. The class DET of problems reducible to integer determinants is defined and many examples given. A new problem complete for deterministic polynomial time is given, namely, finding the lexicographically first maximal clique in a graph. This paper is a revised version of S. A. Cook, (1983, in “Proceedings 1983 Intl. Found. Comut. Sci. Conf.,” Lecture Notes in Computer Science Vol. 158, pp. 78–93, Springer-Verlag, Berlin/New York).
757 citations
TL;DR: This paper shows that the problem of evaluating acyclic Boolean conjunctive queries is complete for LOGCFL, the class of decision problems that are logspace-reducible to a context-free language, and that the acYclic versions of the following well-known database andAI problems are allLOGCFL-complete.
Abstract: This paper deals with the evaluation of acyclic Boolean conjunctive queries in relational databases. By well-known results of Yannakakis[1981], this problem is solvable in polynomial time; its precise complexity, however, has not been pinpointed so far. We show that the problem of evaluating acyclic Boolean conjunctive queries is complete for LOGCFL, the class of decision problems that are logspace-reducible to a context-free language. Since LOGCFL is contained in AC1 and NC2, the evaluation problem of acyclic Boolean conjunctive queries is highly parallelizable. We present a parallel database algorithm solving this problem with alogarithmic number of parallel join operations. The algorithm is generalized to computing the output of relevant classes of non-Boolean queries. We also show that the acyclic versions of the following well-known database and AI problems are all LOGCFL-complete: The Query Output Tuple problem for conjunctive queries, Conjunctive Query Containment, Clause Subsumption, and Constraint Satisfaction. The LOGCFL-completeness result is extended to the class of queries of bounded tree width and to other relevant query classes which are more general than the acyclic queries.
224 citations
TL;DR: This theorem shows that for problems such as arithmetic circuit lower bounds or black-box derandomization of identity testing, the case of depth four circuits is in a certain sense the general case.
179 citations
TL;DR: It is shown that small numbers of “role switches” in two- person pebbling can be eliminated and a general result that shows closure under complementation of classes defined by semi-unbounded fan-in circuits is shown.
Abstract: Following the recent independent proofs of Immerman [SIAM J. Comput., 17 (1988), pp. 935–938] and Szelepcsenyi [Bull. European Assoc. Theoret. Comput. Sci., 33 (1987), pp. 96–100] that nondeterministic space-bounded complexity classes are closed under complementation, two further applications of the inductive counting technique are developed. First, an errorless probabilistic algorithm for the undirected graph s-t connectivity problem that runs in $O(\log n)$ space and polynomial expected time is given. Then it is shown that the class LOGCFL is closed under complementation. The latter is a special case of a general result that shows closure under complementation of classes defined by semi-unbounded fan-in circuits (or, equivalently, nondeterministic auxiliary pushdown automata or tree-size bounded alternating Turing machines). As one consequence, it is shown that small numbers of “role switches” in two-person pebbling can be eliminated.
177 citations
TL;DR: A model of polynomial-time concept prediction is investigated which is a relaxation of the distribution-independent model of concept learning due to Valiant and prediction-preserving reductions are defined and are shown to be effective tools for comparing the relative difficulty of solving various prediction problems.
160 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2020 | 1 |
| 2018 | 3 |
| 2017 | 3 |
| 2016 | 4 |
| 2015 | 2 |