The authors consider the problem of predicting (0, 1)-valued functions on R/sup n/ and smaller domains, based on their values on randomly drawn points. Their model is related to L.G. Valiant's learnability model (1984), but does not require the hypotheses used for prediction to be represented in any specified form. The authors first disregard computational complexity and show how to construct prediction strategies that are optimal to within a constant factor for any reasonable class F of target functions. These prediction strategies use the 1-inclusion graph structure from N. Alon et al.'s work on geometric range queries (1987) to minimize the probability of incorrect prediction. They then turn to computationally efficient algorithms. For indicator functions of axis-parallel rectangles and halfspaces in R/sup n/, they demonstrate how their techniques can be applied to construct computational efficient prediction strategies that are optimal to within a constant factor. They compare the general performance of prediction strategies derived by their method to those derived from existing methods in Valiant's learnability theory.<>
{"title":"Predicting (0, 1)-functions on randomly drawn points","authors":"D. Haussler, N. Littlestone, Manfred K. Warmuth","doi":"10.1109/SFCS.1988.21928","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21928","url":null,"abstract":"The authors consider the problem of predicting (0, 1)-valued functions on R/sup n/ and smaller domains, based on their values on randomly drawn points. Their model is related to L.G. Valiant's learnability model (1984), but does not require the hypotheses used for prediction to be represented in any specified form. The authors first disregard computational complexity and show how to construct prediction strategies that are optimal to within a constant factor for any reasonable class F of target functions. These prediction strategies use the 1-inclusion graph structure from N. Alon et al.'s work on geometric range queries (1987) to minimize the probability of incorrect prediction. They then turn to computationally efficient algorithms. For indicator functions of axis-parallel rectangles and halfspaces in R/sup n/, they demonstrate how their techniques can be applied to construct computational efficient prediction strategies that are optimal to within a constant factor. They compare the general performance of prediction strategies derived by their method to those derived from existing methods in Valiant's learnability theory.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133697290","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}
A general framework for the study of a broad class of communication problems is developed. It is based on a recent analysis of the communication complexity of graph connectivity. The approach makes use of combinatorial lattice theory.<>
{"title":"Lattices, mobius functions and communications complexity","authors":"L. Lovász, M. Saks","doi":"10.1109/SFCS.1988.21924","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21924","url":null,"abstract":"A general framework for the study of a broad class of communication problems is developed. It is based on a recent analysis of the communication complexity of graph connectivity. The approach makes use of combinatorial lattice theory.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133711599","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}
The computational complexity of testing nonemptiness of finite-state automata on infinite trees is investigated. It is shown that for tree automata with m states and n pairs nonemptiness can be tested in time O((mn)/sup 3n/), even though the problem is in general NP-complete. The nonemptiness algorithm is used to obtain exponentially improved, essentially tight upper bounds for numerous important modal logics of programs, interpreted with the usual semantics over structures generated by binary relations. For example, it is shown that satisfiability for the full branching time logic CTL* can be tested in deterministic double exponential time. It also follows that satisfiability for propositional dynamic logic with a repetition construct (PDL-delta) and for the propositional mu-calculus (L mu ) can be tested in deterministic single exponential time.<>
{"title":"The complexity of tree automata and logics of programs","authors":"E. Emerson, C. Jutla","doi":"10.1109/SFCS.1988.21949","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21949","url":null,"abstract":"The computational complexity of testing nonemptiness of finite-state automata on infinite trees is investigated. It is shown that for tree automata with m states and n pairs nonemptiness can be tested in time O((mn)/sup 3n/), even though the problem is in general NP-complete. The nonemptiness algorithm is used to obtain exponentially improved, essentially tight upper bounds for numerous important modal logics of programs, interpreted with the usual semantics over structures generated by binary relations. For example, it is shown that satisfiability for the full branching time logic CTL* can be tested in deterministic double exponential time. It also follows that satisfiability for propositional dynamic logic with a repetition construct (PDL-delta) and for the propositional mu-calculus (L mu ) can be tested in deterministic single exponential time.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116170030","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}
An efficient simulation is given to show that dynamic networks are as fast as static ones up to a constant multiplicative factor. That is, any task can be performed in a dynamic asynchronous network essentially as fast as in a static synchronous network. The simulation protocol is based on an approach in which locality is perceived as the key to fast adaptation to changes in network topology. The heart of the simulation is a technique called a dynamic synchronizer, which achieves 'local' simulation of a global 'clock' in a dynamic asynchronous network. Using this result, improved solutions to a number of well-known problems on dynamic networks are obtained. It can also be used to improve the solution to certain static network problems.<>
{"title":"Dynamic networks are as fast as static networks","authors":"B. Awerbuch, M. Sipser","doi":"10.1109/SFCS.1988.21938","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21938","url":null,"abstract":"An efficient simulation is given to show that dynamic networks are as fast as static ones up to a constant multiplicative factor. That is, any task can be performed in a dynamic asynchronous network essentially as fast as in a static synchronous network. The simulation protocol is based on an approach in which locality is perceived as the key to fast adaptation to changes in network topology. The heart of the simulation is a technique called a dynamic synchronizer, which achieves 'local' simulation of a global 'clock' in a dynamic asynchronous network. Using this result, improved solutions to a number of well-known problems on dynamic networks are obtained. It can also be used to improve the solution to certain static network problems.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116569074","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}
The authors present the first sub-linear-time deterministic parallel algorithms for bipartite matching and several related problems, including maximal node-disjoint paths, depth-first search, and flows in zero-one networks. The results are based on a better understanding of the combinatorial structure of the above problems, which lead to new algorithmic techniques. In particular, it is shown how to use maximal matching to extend, in parallel, a current set of node-disjoint paths and how to take advantage of the parallelism that arises when a large number of nodes are active during an execution of a push/relabel network flow algorithm. It is also shown how to apply the techniques to design parallel algorithms for the weighted versions of the above problems.<>
{"title":"Sublinear-time parallel algorithms for matching and related problems","authors":"A. Goldberg, Serge A. Plotkin, P. M. Vaidya","doi":"10.1109/SFCS.1988.21935","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21935","url":null,"abstract":"The authors present the first sub-linear-time deterministic parallel algorithms for bipartite matching and several related problems, including maximal node-disjoint paths, depth-first search, and flows in zero-one networks. The results are based on a better understanding of the combinatorial structure of the above problems, which lead to new algorithmic techniques. In particular, it is shown how to use maximal matching to extend, in parallel, a current set of node-disjoint paths and how to take advantage of the parallelism that arises when a large number of nodes are active during an execution of a push/relabel network flow algorithm. It is also shown how to apply the techniques to design parallel algorithms for the weighted versions of the above problems.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124207021","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}
Algorithms are developed that adopt a novel implicit representation for multivariate polynomials and rational functions with rational coefficients, that of black boxes for their evaluation. It is shown that within this evaluation-box representation, the polynomial greatest common divisor and factorization problems as well as the problem of extracting the numerator and denominator of a rational function can be solved in random polynomial time in the usual parameters. Since the resulting evaluation programs for the goal polynomials can be converted efficiently to sparse format, solutions to sparse problems such as the sparse ration interpolation problem follow as a consequence.<>
{"title":"Computing with polynomials given by black boxes for their evaluations: greatest common divisors, factorization, separation of numerators and denominators","authors":"E. Kaltofen, B. Trager","doi":"10.1109/SFCS.1988.21946","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21946","url":null,"abstract":"Algorithms are developed that adopt a novel implicit representation for multivariate polynomials and rational functions with rational coefficients, that of black boxes for their evaluation. It is shown that within this evaluation-box representation, the polynomial greatest common divisor and factorization problems as well as the problem of extracting the numerator and denominator of a rational function can be solved in random polynomial time in the usual parameters. Since the resulting evaluation programs for the goal polynomials can be converted efficiently to sparse format, solutions to sparse problems such as the sparse ration interpolation problem follow as a consequence.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131760264","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}
It is shown that a planar st-graph G admits two total orders on the set V union E union F, where V, E, and F are, respectively, the sets of vertices, edges and faces of G, with mod V mod =n. An O(n) space data structure for the maintenance of the two orders is exhibited that supports an update of G (insertion of an edge and expansion of a vertex, and their inverses) in time O(log n). This data structure also supports transitive-closure queries in O(log n). Moreover, planar st-graphs provide the topological underpinning of a fully dynamic planar point location technique in monotone subdivisions, which is an interesting (unique) specialization of the chain method of Lee-Preparata (1977). While maintaining storage O(n) and query time O(log/sup 2/ n), insertion/deletion of a chain with k edges can be done in time O(log/sup 2/ n+k), and insertion/deletion of a vertex on an edge can be done in time O(log n).<>
{"title":"Fully dynamic techniques for point location and transitive closure in planar structures","authors":"F. Preparata, R. Tamassia","doi":"10.1109/SFCS.1988.21972","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21972","url":null,"abstract":"It is shown that a planar st-graph G admits two total orders on the set V union E union F, where V, E, and F are, respectively, the sets of vertices, edges and faces of G, with mod V mod =n. An O(n) space data structure for the maintenance of the two orders is exhibited that supports an update of G (insertion of an edge and expansion of a vertex, and their inverses) in time O(log n). This data structure also supports transitive-closure queries in O(log n). Moreover, planar st-graphs provide the topological underpinning of a fully dynamic planar point location technique in monotone subdivisions, which is an interesting (unique) specialization of the chain method of Lee-Preparata (1977). While maintaining storage O(n) and query time O(log/sup 2/ n), insertion/deletion of a chain with k edges can be done in time O(log/sup 2/ n+k), and insertion/deletion of a vertex on an edge can be done in time O(log n).<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131158257","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}
Interactive proof systems are considered in which the best set of possible verifiers is restricted to the class of probabilistic log-space automata. A. Condon (1988) introduced this model and showed that if the protocols are allowed to run for arbitrarily many rounds, exponential-time languages can be proved to a log-space verifier. To better approximate the usual notion of interactive proof systems, a number of researchers have considered a more realistic, further restricted model in which protocols are polynomially bounded, both in the number of rounds of communication and in the number of computational steps allowed to the verifier. A notion of language-recognition zero-knowledge is defined for this model, and it is shown that anything provable in this model can be proved in language-recognition zero-knowledge.<>
{"title":"Zero-knowledge with log-space verifiers","authors":"J. Kilian","doi":"10.1109/SFCS.1988.21918","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21918","url":null,"abstract":"Interactive proof systems are considered in which the best set of possible verifiers is restricted to the class of probabilistic log-space automata. A. Condon (1988) introduced this model and showed that if the protocols are allowed to run for arbitrarily many rounds, exponential-time languages can be proved to a log-space verifier. To better approximate the usual notion of interactive proof systems, a number of researchers have considered a more realistic, further restricted model in which protocols are polynomially bounded, both in the number of rounds of communication and in the number of computational steps allowed to the verifier. A notion of language-recognition zero-knowledge is defined for this model, and it is shown that anything provable in this model can be proved in language-recognition zero-knowledge.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"9 8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134574639","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}
The author gives efficient parallel algorithms for recognizing chordal graphs, finding a maximum clique and a maximum independent set in a chordal graph, finding an optimal coloring of a chordal graph, finding a breadth-first search tree and a depth-first search tree of a chordal graph, recognizing interval graphs, and testing interval graphs for isomorphism. The key to the results is an efficient parallel algorithm for finding a perfect elimination ordering.<>
{"title":"Efficient parallel algorithms for chordal graphs","authors":"P. Klein","doi":"10.1109/SFCS.1988.21933","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21933","url":null,"abstract":"The author gives efficient parallel algorithms for recognizing chordal graphs, finding a maximum clique and a maximum independent set in a chordal graph, finding an optimal coloring of a chordal graph, finding a breadth-first search tree and a depth-first search tree of a chordal graph, recognizing interval graphs, and testing interval graphs for isomorphism. The key to the results is an efficient parallel algorithm for finding a perfect elimination ordering.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128216588","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}
A two-dimensional array A=(a/sub i,j/) is called monotone if the maximum entry in its ith row lies below or to the right of the maximum entry in its (i- 1)-st row. An array A is called totally monotone if every 2*2 subarray (i.e., every 2*2 minor) is monotone. The notion of two-dimensional totally monotone arrays is generalized to multidimensional arrays, and a wide variety of problems are exhibited involving computational geometry, dynamic programming, VLSI river routing, and finding certain kinds of shortest paths that can be solved efficiently by finding maxima in totally monotone arrays.<>
{"title":"Notes on searching in multidimensional monotone arrays","authors":"A. Aggarwal, James K. Park","doi":"10.1109/SFCS.1988.21966","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21966","url":null,"abstract":"A two-dimensional array A=(a/sub i,j/) is called monotone if the maximum entry in its ith row lies below or to the right of the maximum entry in its (i- 1)-st row. An array A is called totally monotone if every 2*2 subarray (i.e., every 2*2 minor) is monotone. The notion of two-dimensional totally monotone arrays is generalized to multidimensional arrays, and a wide variety of problems are exhibited involving computational geometry, dynamic programming, VLSI river routing, and finding certain kinds of shortest paths that can be solved efficiently by finding maxima in totally monotone arrays.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125158067","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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