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87
Coherence in Finite Argument Systems
, 2001
"... Argument Systems provide a rich abstraction within which divers concepts of reasoning, acceptability and defeasibility of arguments, etc., may be studied using a unified framework. Two important concepts of the acceptability of an argument p in such systems are credulous acceptance to capture the no ..."
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Cited by 67 (25 self)
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Argument Systems provide a rich abstraction within which divers concepts of reasoning, acceptability and defeasibility of arguments, etc., may be studied using a unified framework. Two important concepts of the acceptability of an argument p in such systems are credulous acceptance to capture the notion that p can be `believed'; and sceptical acceptance capturing the idea that if anything is believed, then p must be. One important aspect affecting the computational complexity of these problems concerns whether the admissibility of an argument is defined with respect to `preferred' or `stable' semantics. One benefit of socalled `coherent' argument systems being that the preferred extensions coincide with stable extensions. In this note we consider complexitytheoretic issues regarding deciding if finitely presented argument systems modelled as directed graphs are coherent. Our main result shows that the related decision problem is (p) 2 complete and is obtained solely via the graphtheoretic representation of an argument system, thus independent of the specific logic underpinning the reasoning theory.
On the Computational Complexity of Qualitative Coalitional Games
 Artificial Intelligence
, 2004
"... We study coalitional games in which agents are each assumed to have a goal to be achieved, and where the characteristic property of a coalition is a set of choices, with each choice denoting a set of goals that would be achieved if the choice was made. Such qualitative coalitional games (QCGs) are a ..."
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Cited by 45 (14 self)
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We study coalitional games in which agents are each assumed to have a goal to be achieved, and where the characteristic property of a coalition is a set of choices, with each choice denoting a set of goals that would be achieved if the choice was made. Such qualitative coalitional games (QCGs) are a natural tool for modelling goaloriented multiagent systems. After introducing and formally defining QCGs, we systematically formulate fourteen natural decision problems associated with them, and determine the computational complexity of these problems. For example, we formulate a notion of coalitional stability inspired by that of the core from conventional coalitional games, and prove that the problem of showing that the core of a QCG is nonempty is D 1 complete. (As an aside, we present what we believe is the first "natural" problem that is proven to be complete for D 2 .) We conclude by discussing the relationship of our work to other research on coalitional reasoning in multiagent systems, and present some avenues for future research.
On Balanced vs. Unbalanced Computation Trees
"... A great number of complexity classes between P and PSPACE can be defined via leaf languages for computation trees of nondeterministic polynomial time machines. Jenner, McKenzie, and Th'erien (Proceedings of the 9th Conference on Structure in Complexity Theory, 1994) raised the issue of whether ..."
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Cited by 29 (7 self)
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A great number of complexity classes between P and PSPACE can be defined via leaf languages for computation trees of nondeterministic polynomial time machines. Jenner, McKenzie, and Th'erien (Proceedings of the 9th Conference on Structure in Complexity Theory, 1994) raised the issue of whether considering balanced or unbalanced trees makes any difference. For a number of leaf language classes, coincidence of both models was shown, but for the very prominent example of leaf language classes from the alternating logarithmic time hierarchy the question was left open. It was only proved that in the balanced case these classes exactly characterize the classes from the polynomial time hierarchy. Here, we show that balanced trees apparently make a difference: In the unbalanced case, a class from the logarithmic time hierarchy characterizes the corresponding class from the polynomial time hierarchy with a PPoracle. Along the way, we get an interesting normal form for PP computations.
The Closure of Monadic NP
 Journal of Computer and System Sciences
, 1997
"... It is a wellknown result of Fagin that the complexity class NP coincides with the class of ..."
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Cited by 23 (0 self)
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It is a wellknown result of Fagin that the complexity class NP coincides with the class of
Counting Hierarchies: Polynomial Time And Constant Depth Circuits
, 1990
"... In the spring of 1989, Seinosuke Toda of the University of ElectroCommunications in Tokyo, Japan, proved that the polynomial hierarchy is contained in P PP [To89]. In this Structural Complexity Column, we will briefly review Toda's result, and explore how it relates to other topics of inter ..."
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Cited by 18 (4 self)
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In the spring of 1989, Seinosuke Toda of the University of ElectroCommunications in Tokyo, Japan, proved that the polynomial hierarchy is contained in P PP [To89]. In this Structural Complexity Column, we will briefly review Toda's result, and explore how it relates to other topics of interest in computer science. In particular, we will introduce the reader to The Counting Hierarchy: a hierarchy of complexity classes contained in PSPACE and containing the Polynomial Hierarchy. Threshold Circuits: circuits constructed of MAJORITY gates; this notion of circuit is being studied not only by complexity theoreticians, but also by researchers in an active subfield of AI studying "neural networks". Along the way, we'll review the important notion of an operator on a complexity class. 1. The Counting Hierarchy, and Operators on Complexity Classes The counting hierarchy was defined in [Wa86] and independently by Parberry and Schnitger in [PS88]. (The motivation for [Wa86] was the desir...
Completeness in the polynomialtime hierarchy: A compendium
 SIGACT News
"... We present a Garey/Johnsonstyle list of problems known to be complete for the second and higher levels of the polynomialtime Hierarchy (polynomial hierarchy, or PH for short). We also include the bestknown hardness of approximation results. The list will be updated as necessary. Updates The compe ..."
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Cited by 17 (2 self)
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We present a Garey/Johnsonstyle list of problems known to be complete for the second and higher levels of the polynomialtime Hierarchy (polynomial hierarchy, or PH for short). We also include the bestknown hardness of approximation results. The list will be updated as necessary. Updates The compendium currently lists more than 80 problems. Latest changes include: • added [GT26] SUCCINCT kKING, • added [GT25] SUCCINCT kDIAMETER, • added [GT4] SUCCINCT kRADIUS at third level, • added [GT24] MINIMUM VERTEX COLORING DEFINING SET, • added [GT23] GRAPH SANDWICH PROBLEM FOR Π, • added [L24] MINIMUM 3SAT DEFINING SET,
Database repair by signed formulae
 In Seipel, D., & TurellTorres, J. (Eds.), Proc. 3rd Int. Symp. on Foundations of Information and Knowledge Systems (FoIKS’04), No. 2942 in LNCS
, 2004
"... Abstract. We introduce a simple and practically efficient method for repairing inconsistent databases. The idea is to properly represent the underlying problem, and then use offtheshelf applications for efficiently computing the corresponding solutions. Given a possibly inconsistent database, we r ..."
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Cited by 15 (5 self)
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Abstract. We introduce a simple and practically efficient method for repairing inconsistent databases. The idea is to properly represent the underlying problem, and then use offtheshelf applications for efficiently computing the corresponding solutions. Given a possibly inconsistent database, we represent the possible ways to restore its consistency in terms of signed formulae. Then we show how the ‘signed theory ’ that is obtained can be used by a variety of computational models for processing quantified Boolean formulae, or by constraint logic program solvers, in order to rapidly and efficiently compute desired solutions, i.e., consistent repairs of the database. 1
Logical Approaches to the Complexity of Search Problems: Proof Complexity, Quantified Propositional Calculus, and Bounded Arithmetic
, 2005
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Bounded Arithmetic and Propositional Proof Complexity
 in Logic of Computation
, 1995
"... This is a survey of basic facts about bounded arithmetic and about the relationships between bounded arithmetic and propositional proof complexity. We introduce the theories S 2 of bounded arithmetic and characterize their proof theoretic strength and their provably total functions in terms of t ..."
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Cited by 11 (0 self)
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This is a survey of basic facts about bounded arithmetic and about the relationships between bounded arithmetic and propositional proof complexity. We introduce the theories S 2 of bounded arithmetic and characterize their proof theoretic strength and their provably total functions in terms of the polynomial time hierarchy. We discuss other axiomatizations of bounded arithmetic, such as minimization axioms. It is shown that the bounded arithmetic hierarchy collapses if and only if bounded arithmetic proves that the polynomial hierarchy collapses. We discuss Frege and extended Frege proof length, and the two translations from bounded arithmetic proofs into propositional proofs. We present some theorems on bounding the lengths of propositional interpolants in terms of cutfree proof length and in terms of the lengths of resolution refutations. We then define the RazborovRudich notion of natural proofs of P NP and discuss Razborov's theorem that certain fragments of bounded arithmetic cannot prove superpolynomial lower bounds on circuit size, assuming a strong cryptographic conjecture. Finally, a complete presentation of a proof of the theorem of Razborov is given. 1 Review of Computational Complexity 1.1 Feasibility This article will be concerned with various "feasible" forms of computability and of provability. For something to be feasibly computable, it must be computable in practice in the real world, not merely e#ectively computable in the sense of being recursively computable.
Locating P/poly Optimally in the Extended Low Hierarchy
, 1993
"... The low hierarchy within NP and the extended low hierarchy have turned out to be very useful in classifying many interesting language classes. We relocate P/poly from the third \Sigmalevel EL P;\Sigma 3 (Balc'azar et al., 1986) to the third \Thetalevel EL P;\Theta 3 of the extended low hier ..."
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Cited by 10 (0 self)
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The low hierarchy within NP and the extended low hierarchy have turned out to be very useful in classifying many interesting language classes. We relocate P/poly from the third \Sigmalevel EL P;\Sigma 3 (Balc'azar et al., 1986) to the third \Thetalevel EL P;\Theta 3 of the extended low hierarchy. The location of P=poly in EL P;\Theta 3 is optimal since, as shown by Allender and Hemachandra (1992), there exist sparse sets that are not contained in the next lower level EL P;\Sigma 2 . As a consequence of our result, all NP sets in P=poly are relocated from the third \Sigmalevel L P;\Sigma 3 (Ko and Schoning, 1985) to the third \Thetalevel L P;\Theta 3 of the low hierarchy.