Exponential upper and lower bounds on the size of the cascaded (Krohn-Rhodes) decomposition of automata are given. These results are used to obtain elementary algorithms for various translations between automata and temporal logic, where the previously known translations were nonelementary. The relevance of the result is discussed.<>
{"title":"Tight bounds on the complexity of cascaded decomposition of automata","authors":"O. Maler, A. Pnueli","doi":"10.1109/FSCS.1990.89589","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89589","url":null,"abstract":"Exponential upper and lower bounds on the size of the cascaded (Krohn-Rhodes) decomposition of automata are given. These results are used to obtain elementary algorithms for various translations between automata and temporal logic, where the previously known translations were nonelementary. The relevance of the result is discussed.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"461 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133002261","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 synchronizer is a simulation methodology for simulating a synchronous network by an asynchronous one, thus enabling the execution of a synchronous algorithm on an asynchronous network. Previously known synchronizers require each processor in the network to participate in each pulse of the synchronization process. The resulting communication overhead depends linearly on the number n of network nodes. A synchronizer with overhead only polylogarithmically dependent on n is introduced. This synchronizer can also be realized with polylog(n) space. The polylog-overhead synchronizer is based on involving only the relevant portions of the network in the synchronization process.<>
{"title":"Network synchronization with polylogarithmic overhead","authors":"B. Awerbuch, D. Peleg","doi":"10.1109/FSCS.1990.89572","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89572","url":null,"abstract":"The synchronizer is a simulation methodology for simulating a synchronous network by an asynchronous one, thus enabling the execution of a synchronous algorithm on an asynchronous network. Previously known synchronizers require each processor in the network to participate in each pulse of the synchronization process. The resulting communication overhead depends linearly on the number n of network nodes. A synchronizer with overhead only polylogarithmically dependent on n is introduced. This synchronizer can also be realized with polylog(n) space. The polylog-overhead synchronizer is based on involving only the relevant portions of the network in the synchronization process.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"197 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115479723","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}
Several new complexity classes of search problems that lie between the classes FP and FNP are defined. These classes are contained in the class TFNP of search problems that always have a solution. A problem in each of these new classes is defined in terms of an implicitly given, exponentially large graph, very much like PLS (polynomial local search). The existence of the solution sought is established by means of a simple graph-theoretic lemma with an inefficiently constructive proof. Several class containments and collapses, resulting in the two new classes PDLF contained in PLF are shown; the relation of either class of PLS is open. PLF contains several important problems for which no polynomial-time algorithm is presently known.<>
{"title":"On graph-theoretic lemmata and complexity classes","authors":"C. Papadimitriou","doi":"10.1109/FSCS.1990.89602","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89602","url":null,"abstract":"Several new complexity classes of search problems that lie between the classes FP and FNP are defined. These classes are contained in the class TFNP of search problems that always have a solution. A problem in each of these new classes is defined in terms of an implicitly given, exponentially large graph, very much like PLS (polynomial local search). The existence of the solution sought is established by means of a simple graph-theoretic lemma with an inefficiently constructive proof. Several class containments and collapses, resulting in the two new classes PDLF contained in PLF are shown; the relation of either class of PLS is open. PLF contains several important problems for which no polynomial-time algorithm is presently known.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"23 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120810776","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 show a sharp dichotomy between systems of identical automata with symmetric global control whose behavior is easy to predict and those whose behavior is hard to predict. The division pertains to whether the global control rule is invariant with respect to permutations of the states of the automaton. It is also shown that testing whether the global control rule has this invariance property is an undecidable problem. It is argued that there is a natural analog between complexity in the present model and chaos in dynamical systems.<>
{"title":"On the predictability of coupled automata: an allegory about chaos","authors":"S. Buss, C. Papadimitriou, J. Tsitsiklis","doi":"10.1109/FSCS.1990.89601","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89601","url":null,"abstract":"The authors show a sharp dichotomy between systems of identical automata with symmetric global control whose behavior is easy to predict and those whose behavior is hard to predict. The division pertains to whether the global control rule is invariant with respect to permutations of the states of the automaton. It is also shown that testing whether the global control rule has this invariance property is an undecidable problem. It is argued that there is a natural analog between complexity in the present model and chaos in dynamical systems.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122793711","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 problem of perfectly secure communication in a general network in which processors and communication lines may be faulty is studied. Lower bounds are obtained on the connectivity required for successful secure communication. Efficient algorithms that operate with this connectivity and rely on no complexity theoretic assumptions are derived. These are the first algorithms for secure communication in a general network to achieve simultaneously the goals of perfect secrecy, perfect resiliency, and a worst case time which is linear in the diameter of the network.<>
{"title":"Perfectly secure message transmission","authors":"D. Dolev, C. Dwork, Orli Waarts, M. Yung","doi":"10.1145/138027.138036","DOIUrl":"https://doi.org/10.1145/138027.138036","url":null,"abstract":"The problem of perfectly secure communication in a general network in which processors and communication lines may be faulty is studied. Lower bounds are obtained on the connectivity required for successful secure communication. Efficient algorithms that operate with this connectivity and rely on no complexity theoretic assumptions are derived. These are the first algorithms for secure communication in a general network to achieve simultaneously the goals of perfect secrecy, perfect resiliency, and a worst case time which is linear in the diameter of the network.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"546 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131865288","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 algebraic technique for the construction of interactive proof systems is proposed. The technique is used to prove that every language in the polynomial-time hierarchy has an interactive proof system. For the proof, a method is developed for reducing the problem of verifying the value of a low-degree polynomial at two points to verifying the value at one new point. The results have implications for program checking, verification, and self-correction.<>
{"title":"Algebraic methods for interactive proof systems","authors":"C. Lund, L. Fortnow, H. Karloff, N. Nisan","doi":"10.1145/146585.146605","DOIUrl":"https://doi.org/10.1145/146585.146605","url":null,"abstract":"An algebraic technique for the construction of interactive proof systems is proposed. The technique is used to prove that every language in the polynomial-time hierarchy has an interactive proof system. For the proof, a method is developed for reducing the problem of verifying the value of a low-degree polynomial at two points to verifying the value at one new point. The results have implications for program checking, verification, and self-correction.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128199658","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 maximal number of character comparisons made by a linear-time string matching algorithm, given a text string of length n and a pattern string of length m over a general alphabet, is investigated. The number is denoted by c(n,m) or approximated by (1+C)n, where C is a universal constant. The subscript 'online' is added when attention is restricted to online algorithms, and the superscript '1' is added when algorithms that find only one occurrence of the pattern in the text are considered. It is well known that n>
{"title":"On the exact complexity of string matching","authors":"L. Colussi, Z. Galil, R. Giancarlo","doi":"10.1109/FSCS.1990.89532","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89532","url":null,"abstract":"The maximal number of character comparisons made by a linear-time string matching algorithm, given a text string of length n and a pattern string of length m over a general alphabet, is investigated. The number is denoted by c(n,m) or approximated by (1+C)n, where C is a universal constant. The subscript 'online' is added when attention is restricted to online algorithms, and the superscript '1' is added when algorithms that find only one occurrence of the pattern in the text are considered. It is well known that n<or=c(n,m)<or=2n-m+1 or 0<or=C<or=1. These bounds are improved, and C/sub online/ is determined exactly.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116181962","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}
Several versions of the problem of generating triangular meshes for finite-element methods are studied. It is shown how to triangulate a planar point set or a polygonally bounded domain with triangles of bounded aspect ratio, how to triangulate a planar point set with triangles having no obtuse angles, how to triangulate a point set in arbitrary dimension with simplices of bounded aspect ratio, and how to produce a linear-size Delaunay triangulation of a multidimensional point set by adding a linear number of extra points. All the triangulations have size within a constant factor of optimal and run in optimal time O(n log n+k) with input of size n and output of size k. No previous work on mesh generation simultaneously guarantees well-shaped elements and small total size.<>
{"title":"Provably good mesh generation","authors":"M. Bern, D. Eppstein, J. Gilbert","doi":"10.1109/FSCS.1990.89542","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89542","url":null,"abstract":"Several versions of the problem of generating triangular meshes for finite-element methods are studied. It is shown how to triangulate a planar point set or a polygonally bounded domain with triangles of bounded aspect ratio, how to triangulate a planar point set with triangles having no obtuse angles, how to triangulate a point set in arbitrary dimension with simplices of bounded aspect ratio, and how to produce a linear-size Delaunay triangulation of a multidimensional point set by adding a linear number of extra points. All the triangulations have size within a constant factor of optimal and run in optimal time O(n log n+k) with input of size n and output of size k. No previous work on mesh generation simultaneously guarantees well-shaped elements and small total size.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126794951","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}
Let K be any field, and let F: K/sup n/ to K/sup n/ be a bijection with the property that both F and F/sup -1/ are computable using only arithmetic operations from K. Motivated by cryptographic considerations, the authors concern themselves with the relationship between the arithmetic complexity of F and the arithmetic complexity of F/sup -1/. They give strong relations between the complexity of F and F/sup -1/ when F is an automorphism in the sense of algebraic geometry (i.e. a formal bijection defined by n polynomials in n variables with a formal inverse of the same form). These constitute all such bijections in the case in which K is infinite. The authors show that at polynomially bounded degree, if an automorphism F has a polynomial-size arithmetic circuit, then F/sup -1/ has a polynomial-size arithmetic circuit. Furthermore, this result is uniform in the sense that there is an efficient algorithm for finding such a circuit for F/sup -1/, given such a circuit for F. This algorithm can also be used to check whether a circuit defines an automorphism F. If K is the Boolean field GF(2), then a circuit defining a bijection does not necessarily define an automorphism. However, it is shown in this case that, given any K/sup n/ to K/sup n/ bijection, there always exists an automorphism defining that bijection. This is not generally true for an arbitrary finite field.<>
{"title":"Efficiently inverting bijections given by straight line programs","authors":"Carl Sturtivant, Zhi-Li Zhang","doi":"10.1109/FSCS.1990.89551","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89551","url":null,"abstract":"Let K be any field, and let F: K/sup n/ to K/sup n/ be a bijection with the property that both F and F/sup -1/ are computable using only arithmetic operations from K. Motivated by cryptographic considerations, the authors concern themselves with the relationship between the arithmetic complexity of F and the arithmetic complexity of F/sup -1/. They give strong relations between the complexity of F and F/sup -1/ when F is an automorphism in the sense of algebraic geometry (i.e. a formal bijection defined by n polynomials in n variables with a formal inverse of the same form). These constitute all such bijections in the case in which K is infinite. The authors show that at polynomially bounded degree, if an automorphism F has a polynomial-size arithmetic circuit, then F/sup -1/ has a polynomial-size arithmetic circuit. Furthermore, this result is uniform in the sense that there is an efficient algorithm for finding such a circuit for F/sup -1/, given such a circuit for F. This algorithm can also be used to check whether a circuit defines an automorphism F. If K is the Boolean field GF(2), then a circuit defining a bijection does not necessarily define an automorphism. However, it is shown in this case that, given any K/sup n/ to K/sup n/ bijection, there always exists an automorphism defining that bijection. This is not generally true for an arbitrary finite field.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127899710","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 parallel algorithm for the tree-decomposition problem for fixed width w is presented. The algorithm runs in time O(log/sup 3/ n) and uses O(n) processors on a concurrent-read, concurrent-write parallel random access machine (CRCW PRAM). This result can be used to construct efficient parallel algorithms for three important classes of problems: MS (monadic second-order) properties, linear EMS (extended monadic second-order) extremum problems, and enumeration problems for MS properties, for graphs of tree width at most w. The sequential time complexity of the tree-composition problem for fixed w is improved, and some implications for this improvement are stated.<>
{"title":"Efficient parallel algorithms for tree-decomposition and related problems","authors":"J. Lagergren","doi":"10.1109/FSCS.1990.89536","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89536","url":null,"abstract":"An efficient parallel algorithm for the tree-decomposition problem for fixed width w is presented. The algorithm runs in time O(log/sup 3/ n) and uses O(n) processors on a concurrent-read, concurrent-write parallel random access machine (CRCW PRAM). This result can be used to construct efficient parallel algorithms for three important classes of problems: MS (monadic second-order) properties, linear EMS (extended monadic second-order) extremum problems, and enumeration problems for MS properties, for graphs of tree width at most w. The sequential time complexity of the tree-composition problem for fixed w is improved, and some implications for this improvement are stated.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132026246","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：