Humans appear to be able to learn new concepts without needing to be programmed explicitly in any conventional sense. In this paper we regard learning as the phenomenon of knowledge acquisition in the absence of explicit programming. We give a precise methodology for studying this phenomenon from a computational viewpoint. It consists of choosing an appropriate information gathering mechanism, the learning protocol, and exploring the class of concepts that can be learnt using it in a reasonable (polynomial) number of steps. We find that inherent algorithmic complexity appears to set serious limits to the range of concepts that can be so learnt. The methodology and results suggest concrete principles for designing realistic learning systems.

We determine the exact power of two-prover inter-active proof systems introduced by Ben-Or, Goldwasser, Kilian, and Wigderson (1988). In this system, two all-powerful non-communicating provers convince a randomizing polynomial time verifier in polynomial time that the input z belongs to the language L. It was previously suspected (and proved in a relativized sense) that coNP-complete languages do not admit such proof systems. In sharp contrast, we show that the class of languages having two-prover interactive proof systems is nondeterministic exponential time. After the recent results that all languages in PSPACE have single prover interactive proofs (Lund, Fortnow, Karloff, Nisan, and Shamir), this represents a further step demonstrating the unexpectedly immense power of randomization and interaction in efficient provability. Indeed, it follows that multiple provers with coins are strictly stronger than without, since NEXP # NP. In particular, for the first time, prov-ably polynomial time intractable languages turn out to admit “efficient proof systems’’ since NEXP # P. We show that to prove membership in languages in EXP, the honest provers need the power of EXP only. A consequence, linking more standard concepts of structural complexity, states that if EX P has poly-nomial size circuits then EXP = Cg = MA. The first part of the proof of the main result ex-tends recent techniques of polynomial extrapolation of truth values used in the single prover case. The second part is a verification scheme for multilinearity of an n-variable function held by an oracle and can be viewed as an independent result on program verification. Its proof rests on combinatorial techniques including the estimation of the expansion rate of a graph.

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We study the complexity of the problem of answering queries using materialized views. This problem has attracted a lot of attention recently because of its relevance in data integration. Previous work considered only conjunctive view definitions. We examine the consequences of allowing more expressive view definition languages. The languageswe consider for view definitions and user queries are: conjunctive queries with inequality, positive queries, datalog, and first-order logic. We show that the complexity of the problem depends on whether views are assumed to store all the tuples that satisfy the view definition, or only a subset of it. Finally, we apply the results to the view consistency and view self-maintainability problems which arise in data warehousing. 1 Introduction The notion of materialized view is essential in databases [34] and is attracting more and more attention with the popularity of data warehouses [28]. The problem of answering queries using materialized views [24...

Abstract-This article describes the Boolean satisfiability method for generating test patterns for single stuck-at faults in combinational circuits. This new method generates test patterns in two steps: First, it constructs a formula expressing the Boolean diference between the unfaulted and faulted circuits. Second, it applies a Boolean satisjiability algorithm to the resulting formula. This approach differs from previous methods now in use, which search the circuit structure directly instead of constructing a formula from it. The new method is general and effective: it allows for the addition of heuristics used by structural search methods, and it has produced excellent results on popular test pattern generation benchmarks. I.

Recently several local hill-climbing procedures for propositional satisability havebeen proposed, which are able to solve large and di cult problems beyond the reach ofconventional algorithms like Davis-Putnam. By the introduction of some new variants of these procedures, we provide strong experimental evidence to support the conjecture that neither greediness nor randomness is important in these procedures. One of the variants introduced seems to o er signi cant improvements over earlier procedures. In addition, we investigate experimentally how their performance depends on their parameters. Our results suggest that run-time scales less than simply exponentially in the problem size. 1

\Because nature isn't classical, dammit..."

The paper studies new unit propagation based heuristics for Davis-Putnam-Loveland (DPL) procedure. These are the novel combinations of unit propagation and the usual "Maximum Occurrences in clauses of Minimum Size " heuristics. Based on the experimental evaluations of di erent alternatives a new simple unit propagation based heuristic is put forward. This compares favorably with the heuristics employed in the current state-of-the-art DPL implementations (C-SAT, Tableau, POSIT). 1

. Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case complexity, the threshold phenomenon, known lower bounds for certain classes of algorithms, and the problem of generating hard instances with solutions.

This paper takes the next step in developing the theory of average case complexity initiated by Leonid A Levin. Previous works [Levin 84, Gurevich 87, Venkatesan and Levin 88] have focused on the existence of complete problems. We widen the scope to other basic questions in computational complexity. Our results include: ffl the equivalence of search and decision problems in the context of average case complexity; ffl an initial analysis of the structure of distributional-NP (i.e. NP problems coupled with "simple distributions") under reductions which preserve average polynomial-time; ffl a proof that if all of distributional-NP is in average polynomial-time then non-deterministic exponential-time equals deterministic exponential time (i.e., a collapse in the worst case hierarchy); ffl definitions and basic theorems regarding other complexity classes such as average log-space. An exposition of the basic definitions suggested by Levin and suggestions for some alternative definitions ...