An algorithm is presented for finding an irreducible polynomial of specified degree over a finite field. It is deterministic and runs in polynomial time for fields of small characteristics. A proof is given of the stronger result, that the problem of finding irreducible polynomials of specified degree over a finite field K is deterministic-polynomial-time reducible to the problem of factoring polynomials over the prime field of K.<>
{"title":"New algorithms for finding irreducible polynomials over finite fields","authors":"V. Shoup","doi":"10.1109/SFCS.1988.21944","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21944","url":null,"abstract":"An algorithm is presented for finding an irreducible polynomial of specified degree over a finite field. It is deterministic and runs in polynomial time for fields of small characteristics. A proof is given of the stronger result, that the problem of finding irreducible polynomials of specified degree over a finite field K is deterministic-polynomial-time reducible to the problem of factoring polynomials over the prime field of K.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"1 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":"129338280","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}
David A. McAllester, P. Panangaden, Vasant Shanbhogue
Expressiveness results for indeterminate data flow primitives are established. Choice primitives with three differing fairness assumptions are considered, and it is shown that they are strictly inequivalent in expressive power. It is also shown that the ability to announce choices enhances the expressive power of two of the primitives. These results are proved using a very crude semantics and will thus apply in any reasonable theory of process equivalence.<>
{"title":"Nonexpressibility of fairness and signaling","authors":"David A. McAllester, P. Panangaden, Vasant Shanbhogue","doi":"10.1109/SFCS.1988.21954","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21954","url":null,"abstract":"Expressiveness results for indeterminate data flow primitives are established. Choice primitives with three differing fairness assumptions are considered, and it is shown that they are strictly inequivalent in expressive power. It is also shown that the ability to announce choices enhances the expressive power of two of the primitives. These results are proved using a very crude semantics and will thus apply in any reasonable theory of process equivalence.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"66 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":"131103962","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}
New upper bounds are given for the measure problem of V. Klee (1977) that significantly improve the previous bounds for dimensions greater than 2. An O(n/sup d/2/ log n, n) time-space upper bound to compute the measure of a set of n boxes in Euclidean d-space is obtained. The solution requires several novel ideas including application of the inclusion/exclusion principle, the concept of trellises, streaming, and a partition of d-space.<>
对于V. Klee(1977)的测度问题，给出了新的上界，显著改进了先前的大于2维的上界。得到了一个O(n/sup / d/2/ log n, n)的时空上界，用于计算欧几里得d空间中n个盒子的测度。这个解决方案需要一些新颖的想法，包括包含/排除原则的应用、网格的概念、流和d空间的划分
{"title":"New upper bounds in Klee's measure problem","authors":"M. Overmars, C. Yap","doi":"10.1109/SFCS.1988.21971","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21971","url":null,"abstract":"New upper bounds are given for the measure problem of V. Klee (1977) that significantly improve the previous bounds for dimensions greater than 2. An O(n/sup d/2/ log n, n) time-space upper bound to compute the measure of a set of n boxes in Euclidean d-space is obtained. The solution requires several novel ideas including application of the inclusion/exclusion principle, the concept of trellises, streaming, and a partition of d-space.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"31 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":"115510521","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 complexity of testing whether a finite-state (sequential or concurrent) probabilistic program satisfies its specification expressed in linear temporal logic. For sequential programs an exponential-time algorithm is given and it is shown that the problem is in PSPACE; this improves the previous upper bound by two exponentials and matches the known lower bound. For concurrent programs is is shown that the problem is complete in double exponential time, improving the previous upper and lower bounds by one exponential each. These questions are also addressed for specifications described by omega -automata or formulas in extended temporal logic.<>
{"title":"Verifying temporal properties of finite-state probabilistic programs","authors":"C. Courcoubetis, M. Yannakakis","doi":"10.1109/SFCS.1988.21950","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21950","url":null,"abstract":"The complexity of testing whether a finite-state (sequential or concurrent) probabilistic program satisfies its specification expressed in linear temporal logic. For sequential programs an exponential-time algorithm is given and it is shown that the problem is in PSPACE; this improves the previous upper bound by two exponentials and matches the known lower bound. For concurrent programs is is shown that the problem is complete in double exponential time, improving the previous upper and lower bounds by one exponential each. These questions are also addressed for specifications described by omega -automata or formulas in extended temporal logic.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"20 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":"121281588","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 framework is introduced that provides a unified way for proving correctness as well as analyzing performance of a class of communication protocols called (asynchronous) reset protocols. They are logarithmic transformers, converting protocols working in a static asynchronous network into protocols working in a dynamic asynchronous network. The design of reset protocols is a classical problem in communication networking, renowned for its complexity. A paradigm is developed that gives fresh insight into this complicated problem. This additional insight leads to the development of reset protocols with complexities bounded by the communication complexity of the original protocol.<>
{"title":"On the effects of feedback in dynamic network protocols","authors":"B. Awerbuch","doi":"10.1109/SFCS.1988.21940","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21940","url":null,"abstract":"A framework is introduced that provides a unified way for proving correctness as well as analyzing performance of a class of communication protocols called (asynchronous) reset protocols. They are logarithmic transformers, converting protocols working in a static asynchronous network into protocols working in a dynamic asynchronous network. The design of reset protocols is a classical problem in communication networking, renowned for its complexity. A paradigm is developed that gives fresh insight into this complicated problem. This additional insight leads to the development of reset protocols with complexities bounded by the communication complexity of the original protocol.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"40 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":"123374956","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 some general techniques for establishing the cryptographic strength of a wide variety of games. As case studies, they analyze some weakened versions of the standard forms of oblivious transfer. They also consider variants of oblivious transfer that are motivated by coding theory and physics. Among their results, they show that a noisy telephone line is in fact a very sophisticated cryptographic device. They also present an application to quantum cryptography.<>
{"title":"Achieving oblivious transfer using weakened security assumptions","authors":"C. Crépeau, J. Kilian","doi":"10.1109/SFCS.1988.21920","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21920","url":null,"abstract":"The authors present some general techniques for establishing the cryptographic strength of a wide variety of games. As case studies, they analyze some weakened versions of the standard forms of oblivious transfer. They also consider variants of oblivious transfer that are motivated by coding theory and physics. Among their results, they show that a noisy telephone line is in fact a very sophisticated cryptographic device. They also present an application to quantum cryptography.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"69 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":"122588395","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 simple randomized algorithm is presented for maintaining dynamically evolving binary trees on hypercube networks. The algorithm guarantees that: (1) nodes adjacent in the tree are within distance O(log log N) in an N-processor hypercube, and (2) with overwhelming probability, no hypercube processor is assigned more than O(1+M/N) tree nodes, where M is the number of nodes in the tree. The algorithm is distributed and does not require any global information. This is the first load-balancing algorithm with provably good performance. The algorithm can be used to parallelize efficiently any tree-based computation. It can also be used to maintain efficiently dynamic data structures such as quadtrees. A technique called tree surgery is introduced to deal with dependencies inherent in trees. Together with tree surgery, the study of random walks is used to analyze the algorithm.<>
{"title":"Take a walk, grow a tree","authors":"S. Bhatt, Jin-Yi Cai","doi":"10.1109/SFCS.1988.21963","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21963","url":null,"abstract":"A simple randomized algorithm is presented for maintaining dynamically evolving binary trees on hypercube networks. The algorithm guarantees that: (1) nodes adjacent in the tree are within distance O(log log N) in an N-processor hypercube, and (2) with overwhelming probability, no hypercube processor is assigned more than O(1+M/N) tree nodes, where M is the number of nodes in the tree. The algorithm is distributed and does not require any global information. This is the first load-balancing algorithm with provably good performance. The algorithm can be used to parallelize efficiently any tree-based computation. It can also be used to maintain efficiently dynamic data structures such as quadtrees. A technique called tree surgery is introduced to deal with dependencies inherent in trees. Together with tree surgery, the study of random walks is used to analyze the algorithm.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"18 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":"124786833","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}
Some general techniques are developed for removing randomness from randomized NC algorithms without a blowup in the number of processors. One of the requirements for the application of these techniques is that the analysis of the randomized algorithm uses only pairwise independence. The main new result is a parallel algorithm for the Delta +1 vertex coloring problem with running time O(log/sup 3/ nlog log n) using a linear number of processors on a concurrent-read-concurrent-write parallel random-access machine. The techniques also apply to several other problems, including the maximal-independent-set problem and the maximal-matching problem. The application of the general technique to these last two problems is mostly of academic interest, because NC algorithms using a linear number of processors that have better running times have been previously found.<>
{"title":"Removing randomness in parallel computation without a processor penalty","authors":"M. Luby","doi":"10.1109/SFCS.1988.21934","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21934","url":null,"abstract":"Some general techniques are developed for removing randomness from randomized NC algorithms without a blowup in the number of processors. One of the requirements for the application of these techniques is that the analysis of the randomized algorithm uses only pairwise independence. The main new result is a parallel algorithm for the Delta +1 vertex coloring problem with running time O(log/sup 3/ nlog log n) using a linear number of processors on a concurrent-read-concurrent-write parallel random-access machine. The techniques also apply to several other problems, including the maximal-independent-set problem and the maximal-matching problem. The application of the general technique to these last two problems is mostly of academic interest, because NC algorithms using a linear number of processors that have better running times have been previously found.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"13 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":"127332345","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 multicommodity flow problem is considered where for each pair of vertices (u, v) it is required to send f half-units of commodity (u, v) from u to v and f half-units of commodity (v, u) from v to u without violating capacity constraints. The main result is an algorithm for performing the task provided that the capacity of each cut exceeds the demand across the cut by a Theta (log n) factor. The condition on cuts is required in the worst case, and is trivially within a Theta (log n) factor of optimal for any flow problem. The result can be used to construct the first polylog-times optimal approximation algorithms for a wide variety of problems, including minimum quotient separators, 1/3-2/3 separators, bifurcators, crossing number, and VLSI layout area. It can also be used to route packets efficiently in arbitrary distributed networks.<>
{"title":"An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms","authors":"F. Leighton, Satish Rao","doi":"10.1109/SFCS.1988.21958","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21958","url":null,"abstract":"A multicommodity flow problem is considered where for each pair of vertices (u, v) it is required to send f half-units of commodity (u, v) from u to v and f half-units of commodity (v, u) from v to u without violating capacity constraints. The main result is an algorithm for performing the task provided that the capacity of each cut exceeds the demand across the cut by a Theta (log n) factor. The condition on cuts is required in the worst case, and is trivially within a Theta (log n) factor of optimal for any flow problem. The result can be used to construct the first polylog-times optimal approximation algorithms for a wide variety of problems, including minimum quotient separators, 1/3-2/3 separators, bifurcators, crossing number, and VLSI layout area. It can also be used to route packets efficiently in arbitrary distributed networks.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"12 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":"125963933","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}
Automata on infinite words were introduced by J.R. Buchi (1962) in order to give a decision procedure for S1S, the monadic second-order theory of one successor. D.E. Muller (1963) suggested deterministic omega -automata as a means of describing the behavior of nonstabilising circuits. R. McNaughton (1966) proved that classes of languages accepted by nondeterministic Buchi automata and by deterministic Muller automata are the same. His construction and its proof are quite complicated, and the blow-up of the construction is double exponential. The author presents a determinisation construction that is simpler and yields a single exponent upper bound for the general case. This construction is essentially optimal. It can also be used to obtain an improved complementation construction for Buchi automata that is also optimal. Both constructions can be used to improve the complexity of decision procedures that use automata-theoretic techniques.<>
{"title":"On the complexity of omega -automata","authors":"S. Safra","doi":"10.1109/SFCS.1988.21948","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21948","url":null,"abstract":"Automata on infinite words were introduced by J.R. Buchi (1962) in order to give a decision procedure for S1S, the monadic second-order theory of one successor. D.E. Muller (1963) suggested deterministic omega -automata as a means of describing the behavior of nonstabilising circuits. R. McNaughton (1966) proved that classes of languages accepted by nondeterministic Buchi automata and by deterministic Muller automata are the same. His construction and its proof are quite complicated, and the blow-up of the construction is double exponential. The author presents a determinisation construction that is simpler and yields a single exponent upper bound for the general case. This construction is essentially optimal. It can also be used to obtain an improved complementation construction for Buchi automata that is also optimal. Both constructions can be used to improve the complexity of decision procedures that use automata-theoretic techniques.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"9 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":"128044011","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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