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
A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
Depth reduction for noncommutative arithmetic circuits
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Journal of Algorithms
Local consistency in parallel constraint satisfaction networks
Artificial Intelligence
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
Characterizations of Pushdown Machines in Terms of Time-Bounded Computers
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of 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
Relativized Logspace and Generalized Quantifiers Over Finite Structures
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
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
Theory of Relational Databases
Theory of Relational Databases
The descriptive complexity approach to LOGCFL
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
The complexity of acyclic conjunctive queries
Journal of the ACM (JACM)
Pure Nash equilibria: hard and easy games
Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge
Weighted hypertree decompositions and optimal query plans
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Query answering exploiting structural properties
ACM SIGMOD Record
Tractable database design through bounded treewidth
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Weighted hypertree decompositions and optimal query plans
Journal of Computer and System Sciences
Uniform Constraint Satisfaction Problems and Database Theory
Complexity of Constraints
On the complexity of constrained Nash equilibria in graphical games
Theoretical Computer Science
Pure Nash equilibria: hard and easy games
Journal of Artificial Intelligence Research
Conditional constraint satisfaction: logical foundations and complexity
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Tractable database design and datalog abduction through bounded treewidth
Information Systems
On the power of structural decompositions of graph-based representations of constraint problems
Artificial Intelligence
Structural tractability of constraint optimization
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Dynamic complexity theory revisited
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Hypertree decompositions: structure, algorithms, and applications
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Restricted space algorithms for isomorphism on bounded treewidth graphs
Information and Computation
Hi-index | 5.23 |
The complexity class LOGCFL consists of all languages (or decision problems) which are logspace reducible to a context-free language. Since LOGCFL is included in AC1, the problems in LOGCFL are highly parallelizable. By results of Ruzzo (JCSS 21 (1980) 218), 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 &&egr; 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 (J. Algorithms 16 (1994) 470) 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, we show that the task of computing a tree-decomposition for a graph of constant treewidth is in functional LOGCFL, and thus in AC1. We also show that the following tasks are all highly parallelizable: Computing a solution to an acyclic constraint satisfaction problem; computing an m-coloring for a graph of bounded treewidth; computing the chromatic number and minimal colorings for graphs of bounded tree- width.