Variants of Courcelle's Theorem for complexity classes inside P

2016 ◽  
Vol 3 (1) ◽  
pp. 23-32
Author(s):  
Michael Elberfeld
Keyword(s):  
Complexity Classes ◽  
Courcelle’S Theorem

Logical Decision Problems and Complexity of Logic Programs

1987 ◽  
Vol 10 (1) ◽  
pp. 1-33
Author(s):  
Egon Börger ◽  
Ulrich Löwen
Keyword(s):  
Fixed Point ◽  
Computational Complexity ◽  
Decision Problem ◽  
Decision Problems ◽  
Complexity Classes ◽  
Logic Programs ◽  
Finite Structures ◽  
Syntactic Restrictions

We survey and give new results on logical characterizations of complexity classes in terms of the computational complexity of decision problems of various classes of logical formulas. There are two main approaches to obtain such results: The first approach yields logical descriptions of complexity classes by semantic restrictions (to e.g. finite structures) together with syntactic enrichment of logic by new expressive means (like e.g. fixed point operators). The second approach characterizes complexity classes by (the decision problem of) classes of formulas determined by purely syntactic restrictions on the formation of formulas.

Completeness for nondeterministic complexity classes

1991 ◽  
Vol 24 (1) ◽  
pp. 179-200 ◽  
Author(s):  
Harry Buhrman ◽  
Steven Homer ◽  
Leen Torenvliet
Keyword(s):  
Complexity Classes

scholarly journals Languages that Capture Complexity Classes

1987 ◽  
Vol 16 (4) ◽  
pp. 760-778 ◽  
Author(s):  
Neil Immerman
Keyword(s):  
Complexity Classes

scholarly journals Computing over the Reals with Addition and Order: Higher Complexity Classes

1995 ◽  
Vol 11 (3) ◽  
pp. 358-376 ◽  
Author(s):  
F. Cucker ◽  
P. Koiran
Keyword(s):  
Complexity Classes

Logical Characterizations of Bounded Query Classes I: Logspace Oracle Machines

1993 ◽  
Vol 18 (1) ◽  
pp. 65-92
Author(s):  
Iain A. Stewart
Keyword(s):  
Truth Table ◽  
Complexity Class ◽  
Polynomial Hierarchy ◽  
Complexity Classes ◽  
Turing Machines ◽  
Complete Problems

We consider three sub-logics of the logic (±HP)*[FOs] and show that these sub-logics capture the complexity classes obtained by considering logspace deterministic oracle Turing machines with oracles in NP where the number of oracle calls is unrestricted and constant, respectively; that is, the classes LNP and LNP[O(1)]. We conclude that if certain logics are of the same expressibility then the Polynomial Hierarchy collapses. We also exhibit some new complete problems for the complexity class LNP via projection translations (the first to be discovered: projection translations are extremely weak logical reductions between problems) and characterize the complexity class LNP[O(1)] as the closure of NP under a new, extremely strict truth-table reduction (which we introduce in this paper).

scholarly journals The Computational Complexity of Probabilistic Planning

1998 ◽  
Vol 9 ◽  
pp. 1-36 ◽  
Author(s):  
M. L. Littman ◽  
J. Goldsmith ◽  
M. Mundhenk
Keyword(s):  
Computational Complexity ◽  
Efficient Algorithms ◽  
Boolean Satisfiability ◽  
Complexity Classes ◽  
Probabilistic Planning ◽  
Plan Evaluation ◽  
Partially Ordered ◽  
Boolean Satisfiability Problem ◽  
Complete Problem ◽  
Planning Problems

We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought; we examine totally ordered plans, acyclic plans, and looping plans, and partially ordered plans under three natural definitions of plan value. We show that problems of interest are complete for a variety of complexity classes: PL, P, NP, co-NP, PP, NP^PP, co-NP^PP, and PSPACE. In the process of proving that certain planning problems are complete for NP^PP, we introduce a new basic NP^PP-complete problem, E-MAJSAT, which generalizes the standard Boolean satisfiability problem to computations involving probabilistic quantities; our results suggest that the development of good heuristics for E-MAJSAT could be important for the creation of efficient algorithms for a wide variety of problems.

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