Logical and schematic characterization of complexity classes

1993 ◽  
Vol 30 (1) ◽  
pp. 61-87 ◽  
Author(s):  
Iain A. Stewart
Keyword(s):  
Complexity Classes

scholarly journals Languages recognized by nondeterministic quantum finite automata

2010 ◽  
Vol 10 (9&10) ◽  
pp. 747-770
Author(s):  
Abuzer Yakaryilmaz ◽  
A.C. Cem Say
Keyword(s):  
Finite Automaton ◽  
Finite Automata ◽  
Space Complexity ◽  
Complexity Classes ◽  
Language Recognition ◽  
Closure Properties ◽  
Quantum Finite Automata ◽  
Sublogarithmic Space

The nondeterministic quantum finite automaton (NQFA) is the only known case where a one-way quantum finite automaton (QFA) model has been shown to be strictly superior in terms of language recognition power to its probabilistic counterpart. We give a characterization of the class of languages recognized by NQFAs, demonstrating that it is equal to the class of exclusive stochastic languages. We also characterize the class of languages that are recognized necessarily by two-sided error by QFAs. It is shown that these classes remain the same when the QFAs used in their definitions are replaced by several different model variants that have appeared in the literature. We prove several closure properties of the related classes. The ramifications of these results about classical and quantum sublogarithmic space complexity classes are examined.

scholarly journals A Refined View of Causal Graphs and Component Sizes: SP-Closed Graph Classes and Beyond

2013 ◽  
Vol 47 ◽  
pp. 575-611 ◽  
Author(s):  
C. Bäckström ◽  
P. Jonsson
Keyword(s):  
Domain Size ◽  
Additional Restriction ◽  
Connected Components ◽  
Complexity Classes ◽  
Np Hard ◽  
Causal Graph ◽  
Graph Classes ◽  
Causal Graphs ◽  
Np Hardness

The causal graph of a planning instance is an important tool for planning both in practice and in theory. The theoretical studies of causal graphs have largely analysed the computational complexity of planning for instances where the causal graph has a certain structure, often in combination with other parameters like the domain size of the variables. Chen and Giménez ignored even the structure and considered only the size of the weakly connected components. They proved that planning is tractable if the components are bounded by a constant and otherwise intractable. Their intractability result was, however, conditioned by an assumption from parameterised complexity theory that has no known useful relationship with the standard complexity classes. We approach the same problem from the perspective of standard complexity classes, and prove that planning is NP-hard for classes with unbounded components under an additional restriction we refer to as SP-closed. We then argue that most NP-hardness theorems for causal graphs are difficult to apply and, thus, prove a more general result; even if the component sizes grow slowly and the class is not densely populated with graphs, planning still cannot be tractable unless the polynomial hierachy collapses. Both these results still hold when restricted to the class of acyclic causal graphs. We finally give a partial characterization of the borderline between NP-hard and NP-intermediate classes, giving further insight into the problem.

REFINING KNOWN RESULTS ON THE GENERALIZED WORD PROBLEM FOR FREE GROUPS

1992 ◽  
Vol 02 (02) ◽  
pp. 221-236 ◽  
Author(s):  
IAIN A. STEWART
Keyword(s):  
Word Problem ◽  
Free Groups ◽  
Complexity Classes ◽  
Finitely Generated ◽  
Complete Problem ◽  
Complete Problems

We refine the known result that the generalized word problem for finitely-generated subgroups of free groups is complete for P via logspace reductions and show that by restricting the lengths of the words in any instance and by stipulating that all words must be conjugates then we obtain complete problems for the complexity classes NSYMLOG, NL, and P. The proofs of our results range greatly: some are complexity-theoretic in nature (for example, proving completeness by reducing from another known complete problem), some are combinatorial, and one involves the characterization of complexity classes as problems describable in some logic.

A Complexity Theoretic Parade of Network-Flow-Problems

1988 ◽  
Vol 11 (2) ◽  
pp. 195-208
Author(s):  
Christoph Meinel
Keyword(s):  
Network Flow ◽  
Flow Problem ◽  
Complexity Classes ◽  
Network Flow Problems ◽  
Network Flow Problem ◽  
Flow Problems

In the following we prove the p-projection completeness of a number of extremely restricted modifications of the NETWORK-FLOW-PROBLEM for such well known nonuniform complexity classes like NC1, L, NL, co- NL, P, NP using a branching-program based characterization of these classes given in [Ba86] and [Me86a,b].

Truth definitions in finite models

2004 ◽  
Vol 69 (1) ◽  
pp. 183-200 ◽  
Author(s):  
Leszek Aleksander Kołodziejczyk
Keyword(s):  
Model Checking ◽  
General Theory ◽  
Higher Order ◽  
Fixed Number ◽  
Complexity Classes ◽  
Finite Model ◽  
Sufficient Condition ◽  
First Order ◽  
Truth Definition

AbstractThe paper discusses the notion of finite model truth definitions (or FM-truth definitions), introduced by M. Mostowski as a finite model analogue of Tarski's classical notion of truth definition.We compare FM-truth definitions with Vardi's concept of the combined complexity of logics, noting an important difference: the difficulty of defining FM-truth for a logic does not depend on the syntax of , as long as it is decidable. It follows that for a natural there exist FM-truth definitions whose evaluation is much easier than the combined complexly of would suggest.We apply the general theory to give a complexity-theoretical characterization of the logics for which the classes (prenex classes of higher order logics) define FM-truth. For any d ≥ 2, m ≥ 1 we construct a family of syntactically defined fragments of which satisfy this characterization. We also use the classes to give a refinement of known results on the complexity classes captured by .We close with a few simple corollaries, one of which gives a sufficient condition for the existence, given a vocabulary σ, of a fixed number k such that model checking for all first order sentences over σ can be done in deterministic time nk.

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