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38
The SAT Phase Transition
, 1994
"... : We describe a detailed experimental investigation of the phase transition for several different classes of randomly generated satisfiability problems. We observe a remarkable consistency of features in the phase transition despite the presence in some of the problem classes of clauses of mixed len ..."
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Cited by 59 (7 self)
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: We describe a detailed experimental investigation of the phase transition for several different classes of randomly generated satisfiability problems. We observe a remarkable consistency of features in the phase transition despite the presence in some of the problem classes of clauses of mixed lengths. For instance, each of the problem classes considered has a sharp transition from satisfiable to unsatisfiable problems at a critical value. In addition, there is a common easyhard easy pattern in the difficulty of the problems, with the hardest problems being associated with the phase transition. However, the difficulty of problems of mixed clause lengths is much more variable than that of fixed clause length. Indeed, whilst the median difficulty of random problems of mixed clause lengths can be orders of magnitude easier than that of equivalently sized problems of fixed clause length, the hardest problems of mixed clause lengths can be orders of magnitude harder than the hardest equi...
Tabu Search for SAT
 In Proceedings of AAAI’97
"... In this paper, tabu search for SAT is investigated from an experimental point of view. To this end, TSAT, a basic tabu search algorithm for SAT, is introduced and compared with Selman et al. Random Walk Strategy GSAT procedure, in short RWSGSAT. TSAT does not involve the additional ..."
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Cited by 43 (2 self)
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In this paper, tabu search for SAT is investigated from an experimental point of view. To this end, TSAT, a basic tabu search algorithm for SAT, is introduced and compared with Selman et al. Random Walk Strategy GSAT procedure, in short RWSGSAT. TSAT does not involve the additional
Backbone Fragility and the Local Search Cost Peak
 Journal of Artificial Intelligence Research
, 2000
"... The local search algorithm WSat is one of the most successful algorithms for solving the satisfiability (SAT) problem. It is notably e#ective at solving hard Random 3SAT instances near the socalled `satisfiability threshold', but still shows a peak in search cost near the threshold and large va ..."
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Cited by 39 (3 self)
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The local search algorithm WSat is one of the most successful algorithms for solving the satisfiability (SAT) problem. It is notably e#ective at solving hard Random 3SAT instances near the socalled `satisfiability threshold', but still shows a peak in search cost near the threshold and large variations in cost over di#erent instances. We make a number of significant contributions to the analysis of WSat on highcost random instances, using the recentlyintroduced concept of the backbone of a SAT instance. The backbone is the set of literals which are entailed by an instance. We find that the number of solutions predicts the cost well for smallbackbone instances but is much less relevant for the largebackbone instances which appear near the threshold and dominate in the overconstrained region. We show a very strong correlation between search cost and the Hamming distance to the nearest solution early in WSat's search. This pattern leads us to introduce a measure of the ba...
Rigorous results for random (2 + p)SAT
, 2001
"... In recent years there has been significant interest in the study of random kSAT formulae. For a given set of n Boolean variables, let Bk denote the set of all possible disjunctions of k distinct, noncomplementary literals from its variables (kclauses). A random kSAT formula Fk(n; m) is formed by ..."
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Cited by 17 (3 self)
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In recent years there has been significant interest in the study of random kSAT formulae. For a given set of n Boolean variables, let Bk denote the set of all possible disjunctions of k distinct, noncomplementary literals from its variables (kclauses). A random kSAT formula Fk(n; m) is formed by selecting uniformly and independently m clauses from Bk and taking their conjunction. Motivated by insights from statistical mechanics that suggest a possible relationship between the “order” of phase transitions and computational complexity, Monasson and Zecchina (Phys. Rev. E 56(2) (1997) 1357) proposed the random (2+p)SAT model: for a given p ∈ [0; 1], a random (2 + p)SAT formula, F2+p(n; m), has m randomly chosen clauses over n variables, where pm clauses are chosen from B3 and (1 − p)m from B2. Using the heuristic “replica method” of statistical mechanics, Monasson and Zecchina gave a number of nonrigorous predictions on the behavior of random (2 + p)SAT formulae. In this paper we give the first rigorous results for random (2 + p)SAT, including the following surprising fact: for p 6 2=5, with probability 1 − o(1), a random (2 + p)SAT formula is satis able i its 2SAT subformula is satisfiable. That is, for p 6 2=5, random (2 + p)SAT behaves like random 2SAT.
Scientific benchmarking with temporal logic decision procedures
 In Proc. KR2002
, 2002
"... In this paper we propose a hypothesisdriven design of the empirical analysis of different decision procedures which we refer to as scientific benchmarking. The approach is to start by choosing the benchmark problems for which, on the basis of analytical considerations, we expect a particular decisi ..."
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Cited by 13 (6 self)
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In this paper we propose a hypothesisdriven design of the empirical analysis of different decision procedures which we refer to as scientific benchmarking. The approach is to start by choosing the benchmark problems for which, on the basis of analytical considerations, we expect a particular decision procedure to exhibit a behaviour different from another decision procedure. Then empirical tests are performed in order to verify the particular hypothesis concerning the decision procedures under consideration. As a case study, we apply this methodology to compare different decision procedures for propositional temporal logic. We define two classes of randomly generated temporal logic formulae which we use to investigate the behaviour of two tableauxbased temporal logic approaches using the Logics Workbench, a third tableauxbased approach using the STeP system, and temporal resolution using a new prover called TRP. 1
Probabilistic Performance of a Heuristic for the Satisfiability Problem
 Discrete Applied Mathematics
, 1986
"... An algorithm for the Satisfiability problem is presented and its probabilistic behavior is analysed when combined with two other algorithms studied earlier. The analysis is based on an instance distribution which is parameterized to simulate a variety of sample characteristics. The algorithm dynamic ..."
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Cited by 12 (6 self)
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An algorithm for the Satisfiability problem is presented and its probabilistic behavior is analysed when combined with two other algorithms studied earlier. The analysis is based on an instance distribution which is parameterized to simulate a variety of sample characteristics. The algorithm dynamically assigns values to literals appearing in a given instance until a satisfying assignment is found or the algorithm "gives up" without determining whether or not a solution exists. It is shown that if n clauses are constructed independently from r boolean variables where the probability that a variable appears in a clause as a positive literal is p and as a negative literal is p then almost all randomly generated instances of Satisfiability are solved in polynomial time if p ! :4 ln(n)=r or p ? ln(n)=r or p = c ln(n)=r, :4 ! c ! 1 and lim n;r!1 n 1\Gammac =r 1\Gammaffl ! 1 for any ffl ? 0. It is also shown that if p = c ln(n)=r, :4 ! c ! 1 and lim n;r!1 n 1\Gammac =r = 1 then almost ...
Finding Hard Satisfiability Problems Using Bacterial Conjugation
, 1996
"... The Satisfiability Problem is an important problem, both in Artificial Intelligence and Complexity Theory. Recently, there have been attempts to find efficient algorithms to solve this problem based on the Greedy Algorithm. In order to test these algorithms effectively, hard problems are required. T ..."
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Cited by 10 (0 self)
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The Satisfiability Problem is an important problem, both in Artificial Intelligence and Complexity Theory. Recently, there have been attempts to find efficient algorithms to solve this problem based on the Greedy Algorithm. In order to test these algorithms effectively, hard problems are required. The space of satisfiability problems is enormous and the vast majority of them can be solved trivially, hence the probability of finding hard problems at random is low. Effective methods of finding or constructing hard problems are therefore important in understanding how good the problem solving algorithms actually are. A method of creating hard satisfiability problems by genetic algorithms using mutation and bacterial conjugation is described. Bacterial conjugation is compared with simple mutation. The reasons why traditional bit string representations for this problem are difficult to achieve are discussed. Preliminary results using conjugation are presented and appear to indicate a promis...
On Subclasses of Minimal Unsatisfiable Formulas
 Discrete Applied Mathematics
"... We consider the minimal unsatisfiablity problem MU (k) for propositional formulas in conjunctive normal form (CNF) over n variables and n + k clauses, where k is fixed. It will be shown that MU (k) is in NP. Based on the nondeterministic algorithm we prove for MU(2) that after a simplification by ..."
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Cited by 9 (0 self)
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We consider the minimal unsatisfiablity problem MU (k) for propositional formulas in conjunctive normal form (CNF) over n variables and n + k clauses, where k is fixed. It will be shown that MU (k) is in NP. Based on the nondeterministic algorithm we prove for MU(2) that after a simplification by resolving over variables occuring at most once positively or at most once negatively such minimal unsatisfiable formulas have a simple and unique form. This leads immediately to an algorithm solving the minimal unsatisfiabilty problem for formulas with n+2 clauses in time O(n 3 ). keywords: Propositional formulas, minimal unsatisfiability, 1 Introduction A propositional formula in conjunctive normal form (CNF) is minimal unsatisfiable if and only if the formula is unsatisfiable and deleting an arbitrary clause will result in a satisfiable formula. The problem whether an arbitrary formula in CNF is minimal unsatisfiable is known to be D P complete [PaWo 88], where D P is the class...
Controlled Generation of Hard and Easy Bayesian Networks: Impact on Maximal Clique Tree in Tree Clustering
 Artificial Intelligence
, 2006
"... This article presents and analyzes algorithms that systematically generate random Bayesian networks of varying difficulty levels, with respect to inference using tree clustering. The results are relevant to research on efficient Bayesian network inference, such as computing a most probable explanati ..."
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Cited by 8 (7 self)
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This article presents and analyzes algorithms that systematically generate random Bayesian networks of varying difficulty levels, with respect to inference using tree clustering. The results are relevant to research on efficient Bayesian network inference, such as computing a most probable explanation or belief updating, since they allow controlled experimentation to determine the impact of improvements to inference algorithms. The results are also relevant to research on machine learning of Bayesian networks, since they support controlled generation of a large number of data sets at a given difficulty level. Our generation algorithms, called BPART and MPART, support controlled but random construction of bipartite and multipartite Bayesian networks. The Bayesian network parameters that we vary are the total number of nodes, degree of connectivity, the ratio of the number of nonroot nodes to the number of root nodes, regularity of the underlying graph, and characteristics of the conditional probability tables. The main dependent parameter is the size of the maximal clique as generated by tree clustering. This article presents extensive empirical analysis using the H��� � tree clustering approach as well as theoretical analysis related to the random generation of Bayesian networks using BPART and MPART. 1
Conjugation  A Bacterially Inspired Form of Genetic Recombination
 Stanford University
"... Bacterial Conjugation is a process that involves the unidirectional transfer of genetic information by direct cellular contact from a donor bacterial cell to a recipient bacterial cell. This paper describes a genetic recombination operator inspired by bacterial conjugation. Three forms of conjugati ..."
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Cited by 8 (0 self)
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Bacterial Conjugation is a process that involves the unidirectional transfer of genetic information by direct cellular contact from a donor bacterial cell to a recipient bacterial cell. This paper describes a genetic recombination operator inspired by bacterial conjugation. Three forms of conjugation are described: a simulation of the direct cellular contact using a matrix of forms that exchange genetic material when adjacent in the matrix. Secondly, the simple conjugation operator is described and finally a method of recombination based on tournament selection is introduced. Category: Genetic Algorithms 1 Introduction Conjugation in bacteria involves the unidirectional transfer of genetic material by direct cellular contact between a donor bacterial cell and a recipient cell. Initially a bridge is formed connecting both cells. Following this, a segment of the donor's chromosome is transferred across into the recipient cell and may undergo genetic recombination with a similar genet...