L. Stockmeyer. Classifying the computational complexity of problems. Journal of Symbolic Logic, 52:1--43, 1987. Home/Search Document Not in Database Summary Related Articles Check |
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A Hierarchy of Modal Event Calculi: Expressiveness and .. - Cervesato.. (1997) (Correct)
....either a polynomial check, or an NP check, or a co NP check. This means that it can be computed by a Turing machine which can acces an NP oracle and runs in deterministic polynomial time, and hence the problem is in P (since only one call to the oracle is needed, it is actually in P NP [1] [15]. We are currently working at the characterization of the exact complexity of model checking in both ICMEC and GMEC . Another issue of interest when working with EC and in its modal refinements is the generation of MVIs, which can be solved using the same logic programs that implement model ....
L. Stockmeyer. "Classifying the computational complexity of problems", Journal of Symbolic Logic, 52(1), 1987, 1--43. This article was processed using the L A T E X macro package with LLNCS style
The Complexity of Temporal Logic Model Checking - Schnoebelen (2002) (2 citations) (Correct)
....model checking and the underlying algorithmic ideas. This covers the main temporal logics encountered in the programming literature: LTL (from [GPSS80] We assume the reader has some basic knowledge of the theoretical framework of computational complexity, and refer him to standard texts like [Sto87, Joh90, Pap94] for more motivations and details. CTL (from [CE81] CTL # (from [EH86] their fragments, and their extensions with past time modalities . The presentation is mainly focused on complexity results, not on the usefulness, or elegance, or expressive power, of the temporal logics ....
L. J. Stockmeyer. Classifying the computational complexity of problems. The Journal of Symbolic Logic, 52:143, 1987.
Linear Logic and Computation: A Survey - Scedrov (1993) (2 citations) (Correct)
....follows from current work of Lincoln and Shankar [26] see below. The hardness proof in [24] combines E. Shapiro s logic programming simulation of nondeterministic Turing machines [34] with the standard proof of the pspace hardness of quantified boolean formula validity as in, e.g. Stockmeyer [35], and utilizing some of the remarkable plasticity of linear logic. The hardness result is achieved through a direct encoding of Turing machine transitions, which are shared via the additives, and the existential quantification over intermediate Turing machine configurations. The linear depth bound ....
L. Stockmeyer. Classifying the computational complexity of problems. Journal of Symbolic Logic, 52:1--43, 1987.
Abduction from Logic Programs: Semantics and Complexity - Eiter, Gottlob, Leone (1998) (14 citations) (Correct)
....unique stable model of LP . As a consequence, j= wf , j= b st , and j= c st are all equivalent on stratified programs. 2. 2 Complexity Theory For NP completeness and complexity theory, cf. 56] The classes Sigma P k ; Pi P k and Delta P k of the Polynomial Hierarchy (PH) cf. [75]) are defined as follows: Delta P 0 = Sigma P 0 = Pi P 0 = P and for all k 1, Delta P k = P Sigma P k Gamma1 ; Sigma P k = NP Sigma P k Gamma1 ; Pi P k = co Sigma P k : In particular, NP = Sigma P 1 , co NP = Pi P 1 , and Delta P 2 = P NP . Here P C ....
....abduction from logic programming, a topic of increasing interest, provides a rich variety of complete problems for a number of slots within the polynomial hierarchy. This gives support to the original belief that the polynomial hierarchy would be useful for classifying computational problems, cf. [75]. Briefly, the following conclusions can be drawn. Abduction from logic programs has the same complexity for well founded inference (j= wf ) and the brave variant of stable inference (j= b st ) excepting the verification of a given solution, which is polynomial under the former and NP complete ....
L. Stockmeyer. Classifying the Computational Complexity of Problems. Journal of Symbolic Logic, 52(1):1--43, 1987.
What is an Inference Rule? - Fagin, Halpern, Vardi (1992) (Correct)
....where we provide some of the basic definitions. Those readers who are familiar with complexity theory can skip it. For a more comprehensive introduction to complexity theory, we refer the reader to books by Hopcroft and Ullman [HU79] and by Garey and Johnson [GJ79] and a paper by Stockmeyer [Sto87]. Formally, we view everything in terms of the difficulty of determining membership in a set. For example, the problem of deciding whether oe v in propositional logic is viewed as the problem of determining whether a given possible validity inference oe v is a member of the set of all ....
L. J. Stockmeyer. Classifying the computational complexity of problems. Journal of Symbolic Logic, 52:1--43, 1987. 32
The Complexity of Nested Counterfactuals and Iterated.. - Eiter, Gottlob (1993) (7 citations) (Correct)
....counterfactuals is one of few genuine natural problems known to be complete for this class. This result and other results contribute to warrant the originally expected use of the classes of the polynomial hierarchy for classifying the complexity of natural problems, which was called in question [33]. Iterated left nesting seems to increase complexity, but it is not clear whether it can give all of PSPACE. It is conjectured that the given upper bounds are sharp. Note that negation in left nesting, as opposed to right nesting, does not increase complexity; in particular, evaluating ( p q) ....
L. Stockmeyer. Classifying the Computational Complexity of Problems. Journal of Symbolic Logic, 52(1):1--43, 1987.
How Hard is it to Revise a Belief Base? - Nebel (1996) (Correct)
.... 10.3 Discussion The extensive complexity analysis of different variants of base revision schemes and related problems has a value in itself, because it provides us with many natural problems located in the lower end of the polynomial hierarchy something which was thought to be unlikely [ Stockmeyer, 1987 ] However, it also helps us to relate it to other, similar problems, to identify sources of complexity, and to identify subproblems that are easily solvable [ Nebel, 1996 ] In summary, we get a much better understanding of the problem and its hard and easy to solve aspects, which helps us to ....
Larry Stockmeyer. Classifying the computational complexity of problems. Journal of Symbolic Logic, 52(1):1--43, 1987.
Enhancing Disjunctive Datalog by Constraints - Buccafurri, Leone, Rullo (1999) (17 citations) (Correct)
....model semantics [20, 46] which is a widely acknowledged semantics for normal and disjunctive Datalog programs. 4. 1 Preliminaries on Complexity Theory For NP completeness and complexity theory, cf. 41] The classes Sigma P k ; Pi P k and Delta P k of the Polynomial Hierarchy (PH) cf. [53]) are defined as follows: Delta P 0 = Sigma P 0 = Pi P 0 = P and for all k 1, Delta P k = P Sigma P k Gamma1 ; Sigma P k = NP Sigma P k Gamma1 ; Pi P k = co Sigma P k : In particular, NP = Sigma P 1 , co NP = Pi P 1 , and Delta P 2 = P NP . Here P C (resp. ....
Stockmeyer, L. (1987) Classifying the Computational Complexity of Problems,. Journal of Symbolic Logic, 52(1), 1--43.
Complexity Classes - Allender, Loui, Regan (Correct)
....1974 ] is called WS1S. We need not be concerned with any details of this logic. Stockmeyer showed that any circuit that takes as input a formula with up to 616 symbols and produces as output a correct answer saying whether the formula is valid, requires at least 10 123 gates. According to [ Stockmeyer, 1987 ] Even if gates were the size of a proton and were connected by infinitely thin wires, the network would densely fill the known universe. Of course, Stockmeyer s theorem holds for one particular sort of circuitry, but the awesome size of the lower bound makes it evident that, no matter how ....
L. Stockmeyer. Classifying the computational complexity of problems. J. Symb. Logic, 52:1--43, 1987.
A Hierarchy of Modal Event Calculi: Expressiveness and .. - Cervesato.. (1997) (Correct)
....a polynomial check, or an NP check, or a co NP check. This means that it can be computed by a Turing machine which can acces an NP oracle and runs in deterministic polynomial time, and hence the problem is in P NP (since only one call to the oracle is needed, it is actually in P NP [1] [15]. We are currently working at the characterization of the exact complexity of model checking in both ICMEC and GMEC . Another issue of interest when working with EC and in its modal refinements is the generation of MVIs, which can be solved using the same logic programs that implement model ....
L. Stockmeyer. "Classifying the computational complexity of problems", Journal of Symbolic Logic, 52(1), 1987, 1--43. This article was processed using the L A T E X macro package with LLNCS style
Capturing Complexity Classes with Lindström Quantifiers - Makowsky (1994) (Correct)
....Logics and Complexity Classes. Joint work with Y.B. Pnueli) In the last 20 years several logics were exhibited which capture complexity classes such as L (LogSpace) NL (Non deterministic LogSpace) P (Polynomial Time) NP (Non deterministic Polynomial Time) PH (the polynomial hierarchy) [Fag74, Imm87, Imm89, Sto87, Ste91]. In mathematical logic the theory of abstract model theory and Lindstrom quantifiers is well established [BF85] In this talk we report our work concerning unification of Descriptive Complexity Theory and Abstract Model Theory. A detailed account has been published in [MP93, MP94] Lindstrom ....
L. Stockmeyer. Classifying the computational complexity of problems. Journal of Symbolic Logic, 52(1):1--43, 1987.
First Order Linear Logic without Modalities Is NEXPTIME-Hard - Lincoln, Scedrov (1994) (9 citations) (Correct)
....(single) exponential time Turing machines are given in Section 2. An encoding of nondeterministic exponential time Turing machines by mall1 formulas is given in Section 3. This encoding is reminiscent of the standard proof of the pspace hardness of quantified boolean formula validity [28, 16]. The encoding is also related to the logic programming simulation of Turing machines given in [27] In Section 4 it is shown that whenever a nondeterministic exponential time Turing machine accepts, then the mall1 formula encoding the machine is provable. The converse is shown in Section 5. We ....
....there exists a polynomial p(n) with nonnegative integer coefficients such that M 2 ntime(2 p(n) that is, for each t 2 L(M ) M accepts t in at most 2 p(n) steps, where n is the length of t. Let nexptime be the class of languages of the form L(M) for some exponential time Turing machine M [28]. 3 ENCODING NEXPTIME IN MALL1 10 3 Encoding nexptime in mall1 In this section we give an efficient encoding of any nondeterministic Turing machine and any input by a mall1 sequent, which also depends on a natural number n. In Sections 4 and 5 it will be shown that the mall1 sequent is provable ....
L. Stockmeyer. Classifying the computational complexity of problems. Journal of Symbolic Logic, 52:1--43, 1987.
Weakly Hard Problems - Lutz (1994) (10 citations) (Correct)
....1 Introduction In practice to date, proving that a decision problem (i.e. language) H f0; 1g is computationally intractable usually amounts to proving that every member of the complexity class E = DTIME(2 linear ) or some larger class is efficiently reducible to H. See [25] for a survey of such arguments. For example, some problems involving the existence of winning strategies for certain two person combinatorial games are known to be intractable because they are polynomial time many one hard (in fact, logarithmic space manyone complete) for E [24] Briefly, a ....
L. J. Stockmeyer, Classifying the computational complexity of problems, Journal of Symbolic Logic 52 (1987), pp. 1--43.
First Order Linear Logic without Modalities is NEXPTIME-Hard - Lincoln, Scedrov (1994) (9 citations) (Correct)
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L. Stockmeyer. Classifying the computational complexity of problems. Journal of Symbolic Logic, 52:1--43, 1987.
Weakly Hard Problems - Jack Lutz Department (1994) (10 citations) (Correct)
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L. J. Stockmeyer, Classifying the computational complexity of problems, Journal of Symbolic Logic 52 (1987), pp. 1--43. 30
On the Indiscernibility of Individuals in Logic Programming - Eiter, Gottlob, Leone (1996) (Correct)
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L. Stockmeyer. Classifying the Computational Complexity of Problems. Journal of Symbolic Logic, 52(1):1-43, 1987.
Complexity Theory - Allender, Loui, Regan (2004) (Correct)
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Stockmeyer, L.J. 1987. Classifying the computational complexity of problems. J. Symb. Logic, 52, 1--43.
Complexity Classes - Allender, Loui, Regan (Correct)
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L. Stockmeyer. Classifying the computational complexity of problems. J. Symb. Logic, 52:1--43, 1987.
How Many Variables Does One Need to Prove PSPACE-hardness of .. - Chagrov, Rybakov (2003) (Correct)
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L. Stockmeyer. Classifying the computational complexity of problems. The Journal of Symbolic Logic, 52(1):1-43, 1987.
On the Indiscernibility of Individuals in Logic Programming - Eiter, Gottlob, Leone (1997) (Correct)
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L. Stockmeyer. Classifying the Computational Complexity of Problems. Journal of Symbolic Logic, 52(1):1-43, 1987.
What is an Inference Rule? - Fagin, Halpern, Vardi (1992) (Correct)
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L. J. Stockmeyer. Classifying the computational complexity of problems. Journal of Symbolic Logic, 52:1-43, 1987.
Provability in TBLL: A Decision Procedure - Chirimar, Lipton (1993) (4 citations) (Correct)
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Stockmeyer, L. [1987] "Classifying the computational complexity of problems", Journal of Symbolic Logic, volume 52, pp. 1-43.
Provability in TBLL: A Decision Procedure - Chirimar, Lipton (1993) (4 citations) (Correct)
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Stockmeyer, L. [1987] "Classifying the computational complexity of problems", Journal of Symbolic Logic, volume 52, pp. 1-43.
The Complexity of Enhanced Path-Based Defeasible.. - Xianchang Wang Jia-Huai (Correct)
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L. Stockmeyer. Classifying the computational complexity of problems. Journal of Symbolic Logic, 52:1--43, 1987.
Other Complexity Classes and Measures - Allender, Loui, Regan (1999) (Correct)
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L. Stockmeyer. Classifying the computational complexity of problems. J. Symb. Logic, 52:1--43, 1987.
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