Two applications of inductive counting for complementation problems
SIAM Journal on Computing
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Properties that characterize LOGCFL
Journal of Computer and System Sciences
Depth reduction for noncommutative arithmetic circuits
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Journal of Algorithms
Parallel Algorithms with Optimal Speedup for Bounded Treewidth
SIAM Journal on Computing
Non-commutative arithmetic circuits: depth reduction and size lower bounds
Theoretical Computer Science
On the Complexity of General Context-Free Language Parsing and Recognition (Extended Abstract)
Proceedings of the 6th Colloquium, on Automata, Languages and Programming
Collapsing Oracle-Tape Hierarchies
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
The Complexity of Acyclic Conjunctive Queries
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
The descriptive complexity approach to LOGCFL
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
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By results of Ruzzo [13], the complexity class LOGCFL can be characterized as the class of languages accepted by alternating Turing Machines (ATMs) which use logarithmic space and have polynomially sized accepting computation trees. We show that for each such ATM M recognizing a language A in LOGCFL, it is possible to construct an LLOGCFL transducer TM such that TM on input w ∈ A outputs an accepting tree for M on w. It follows that computing single LOGCFL certificates is feasible in functional AC1 and is thus highly parallelizable. Wanke [17] has recently shown that for any fixed k, deciding whether the treewidth of a graph is at most k is in the complexity-class LOGCFL. As an application of our general result, it follows that the task of computing a tree-decomposition for a graph of constant treewidth is in functional LOGCFL, and thus in AC1. Similar results apply to many other important search problems corresponding to decision problems in LOGCFL.