{"title":"Disjunctions of Horn Theories and Their Cores","authors":"Thomas Eiter, T. Ibaraki, K. Makino","doi":"10.1137/S0097539799350840","DOIUrl":"https://doi.org/10.1137/S0097539799350840","url":null,"abstract":"In this paper, we study issues on disjunctions of propositional Horn theories. In particular, we consider deciding whether a disjunction of Horn theories is Horn, and, if not, computing a Horn core, i.e., a maximal Horn theory included in this disjunction. The problems are investigated for different representations of Horn theories, namely for Horn CNFs and characteristic models. While the problems are shown to be intractable in general, we present polynomial time algorithms for bounded disjunctions in the formula-based case.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126459268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Compactness of Interval Routing for Almost All Graphs","authors":"C. Gavoille, D. Peleg","doi":"10.1137/S0097539799351717","DOIUrl":"https://doi.org/10.1137/S0097539799351717","url":null,"abstract":"Interval routing is a compact way for representing routing tables on a graph. It is based on grouping together, in each node, destination addresses that use the same outgoing edge in the routing table. Such groups of addresses are represented by some intervals of consecutive integers. We show that almost all the graphs, i.e., a fraction of at least 1− 1/n 2 of all the n-node graphs, support a shortest path interval routing with at most three intervals per outgoing edge, even if the addresses of the nodes are arbitrarily fixed in advance and cannot be chosen by the designer of the routing scheme. In case the addresses are initialized randomly, we show that two intervals per outgoing edge suffice, and conversely, that two intervals are required, for almost all graphs. Finally, if the node addresses can be chosen as desired, we show how to design in polynomial time a shortest path interval routing with a single interval per outgoing edge, for all but at most O(log3 n) outgoing edges in each node. It follows that almost all graphs support a shortest path routing scheme which requires at most n + O(log4 n) bits of routing information per node, improving on the previous upper bound.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127887014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Determinization of Weighted Finite Automata","authors":"A. Buchsbaum, R. Giancarlo, J. Westbrook","doi":"10.1137/S0097539798346676","DOIUrl":"https://doi.org/10.1137/S0097539798346676","url":null,"abstract":"We study the problem of constructing the deterministic equivalent of a nondeterministic weighted finite-state automaton (WFA). Determinization of WFAs has important applications in automatic speech recognition (ASR). We provide the first polynomial-time algorithm to test for the twins property, which determines if a WFA admits a deterministic equivalent. We also give upper bounds on the size of the deterministic equivalent; the bound is tight in the case of acyclic WFAs. Previously, Mohri presented a superpolynomial-time algorithm to test for the twins property, and he also gave an algorithm to determinize WFAs. He showed that the latter runs in time linear in the size of the output when a deterministic equivalent exists; otherwise, it does not terminate. Our bounds imply an upper bound on the running time of this algorithm. \u0000Given that WFAs can expand exponentially in size when determinized, we explore why those that occur in ASR tend to shrink when determinized. According to ASR folklore, this phenomenon is attributable solely to the fact that ASR WFAs have simple topology, in particular, that they are acyclic and layered. We introduce a very simple class of WFAs with this structure, but we show that the expansion under determinization depends on the transition weights: some weightings cause them to shrink, while others, including random weightings, cause them to expand exponentially. We provide experimental evidence that ASR WFAs exhibit this weight dependence. That they shrink when determinized, therefore, is a result of favorable weightings in addition to special topology. These analyses and observations have been used to design a new, approximate WFA determinization algorithm, reported in a separate paper along with experimental results showing that it achieves significant WFA size reduction with negligible impact on ASR performance.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123140631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The CREW PRAM Complexity of Modular Inversion","authors":"J. Gathen, I. Shparlinski","doi":"10.1137/S0097539797328070","DOIUrl":"https://doi.org/10.1137/S0097539797328070","url":null,"abstract":"One of the long-standing open questions in the theory of parallel computation is the parallel complexity of the integer gcd and related problems, such as modular inversion. We present a lower bound Ω(log n) for the CREW PRAM complexity for inversion modulo certain n-bit integers, including all such primes. For infinitely many moduli, our lower bound matches asymptotically the known upper bound. We obtain a similar lower bound for computing a specified bit in a large power of an integer. Our main tools are certain estimates for exponential sums in finite fields.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124092938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An Algorithm for Heilbronn's Problem","authors":"C. Bertram-Kretzberg, T. Hofmeister, H. Lefmann","doi":"10.1137/S0097539798348870","DOIUrl":"https://doi.org/10.1137/S0097539798348870","url":null,"abstract":"Heilbronn conjectured that given arbitrary n points from R2, located in the unit square (or disc), there must be three points which form a triangle of area at most O(1/n2). This conjecture was shown to be false by a nonconstructive argument of Komlos, Pintz and Szemeredi [6] who showed that for every n there is a configuration of n points in the unit square where all triangles have area at least Ω(log n/n2). In this paper, we provide a polynomial-time algorithm which for every n computes such a configuration of n points.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128503146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Combinatorial Consistency Lemma with Application to Proving the PCP Theorem","authors":"Oded Goldreich, S. Safra","doi":"10.1137/S0097539797315744","DOIUrl":"https://doi.org/10.1137/S0097539797315744","url":null,"abstract":"The current proof of the PCP Theorem (i.e., NP=PCP (log, O(1))) is very complicated. One source of difficulty is the technically involved analysis of low-degree tests. Here, we refer to the difficulty of obtaining strong results regarding low-degree tests; namely, results of the type obtained and used by Arora and Safra and Arora et. al.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122685743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Tree Contractions and Evolutionary Trees","authors":"M. Kao","doi":"10.1137/S0097539795283504","DOIUrl":"https://doi.org/10.1137/S0097539795283504","url":null,"abstract":"An evolutionary tree is a rooted tree where each internal vertex has at least two children and where the leaves are labeled with distinct symbols representing species. Evolutionary trees are useful for modeling the evolutionary history of species. An agreement subtree of two evolutionary trees is an evolutionary tree which is also a topological subtree of the two given trees. We give an algorithm to determine the largest possible number of leaves in any agreement subtree of two trees T1 and T2 with n leaves each. If the maximum degree d of these trees is bounded by a constant, the time complexity is O(n log2n) and is within a log n factor of optimal. For general d, this algorithm runs in O(nd2 log d log2n) time or alternatively in O(nd√d log3n) time.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"765 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132051292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Equivalence of Measures of Complexity Classes","authors":"Josef M. Breutzmann, J. H. Lutz","doi":"10.1137/S0097539796302269","DOIUrl":"https://doi.org/10.1137/S0097539796302269","url":null,"abstract":"The resource-bounded measures of complexity classes are shown to be robust with respect to certain changes in the underlying probability measure. Specifically, for any real number δ > 0, any uniformly polynomial-time computable sequence β=(β0,β1,β2), ... of real numbers (biases) β i e [δ, 1−δ], and any complexity class C (such as P, NP, BPP, P/Poly, PH, PSPACE, etc.) that is closed under positive, polynomial-time, truth-table reductions with queries of at most linear length, it is shown that the following two conditions are equivalent.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122121828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Inverse Satisfiability Problem","authors":"D. Kavvadias, M. Sideri","doi":"10.1137/S0097539795285114","DOIUrl":"https://doi.org/10.1137/S0097539795285114","url":null,"abstract":"We study the complexity of telling whether a set of bitvectors represents the set of all satisfying truth assignments of a Boolean expression of a certain type. We show that the problem is coNP-complete when the expression is required to be in conjunctive normal form with three literals per clause (3CNF). We also prove a Dichotomy Theorem analogous to the classical one by Schaefer, stating that, unless P=NP, the problem can be solved in polynomial time if and only if the clauses allowed are either all Horn, or all anti-Horn, or all 2CNF, or all equivalent to equations modulo two.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127168031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An On-Line Algorithm for Some Uniform Processor Scheduling","authors":"Rongheng Li, Lijie Shi","doi":"10.1137/S0097539799527969","DOIUrl":"https://doi.org/10.1137/S0097539799527969","url":null,"abstract":"This paper considers the problem of on-line scheduling a set of independent jobs on m uniform machines (M1, M2,⋯, Mm) in which machine M′is processing speed is si=1(i=1,⋯, m−1) and sm=s>1. List Scheduling [Yookum Cho and Sartaj Sahni. Bounds for list schedules on uniform processors. SIAM J. Compute. 9(1980), pp91–103.] guarantees a worst case performance of 3m−1/m+1(m≥3) and 1+√5/2(m=2) for this problem.We prove that this worst case bound cannot be imporved for m=2 and m=3 and for every m≥4, an algorithm with worst case performance at most 3m−1/m+1−e is presented when sm=2, where e is a fixed positive number, and then we improve the bound for general sm=s>1.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"158 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123098014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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