Results in recursion-theoretic inductive inference have been criticized as depending on unrealistic self-referential examples. J.M. Barzdin (1974) proposed a way of ruling out such examples and conjectured that one of the earliest results of inductive inference theory would fall if his method were used. The author refutes Barzdin's conjecture and proposes a new line of research examining robust separations which are defined using a strengthening of Barzdin's original idea. Preliminary results are presented, and the most important open problem is stated as a conjecture. The extension of this work from function learning to formal language learning is discussed.<>
{"title":"Robust separations in inductive inference","authors":"Mark A. Fulk","doi":"10.2178/jsl/1305810752","DOIUrl":"https://doi.org/10.2178/jsl/1305810752","url":null,"abstract":"Results in recursion-theoretic inductive inference have been criticized as depending on unrealistic self-referential examples. J.M. Barzdin (1974) proposed a way of ruling out such examples and conjectured that one of the earliest results of inductive inference theory would fall if his method were used. The author refutes Barzdin's conjecture and proposes a new line of research examining robust separations which are defined using a strengthening of Barzdin's original idea. Preliminary results are presented, and the most important open problem is stated as a conjecture. The extension of this work from function learning to formal language learning is discussed.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"11 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":"126800169","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}
Two deterministic routing networks, the pruned butterfly and the sorting fat-tree, are presented. Both networks are area universal, i.e. they can simulate with polylogarithmic slowdown, any other routing network fitting in similar area. Previous area-universal networks were either for the offline problem, where the message set to be routed is known in advance and substantial precomputation is permitted, or involved randomization, yielding results that hold only with high probability. The present networks are the first that are simultaneously deterministic and online, and they use two substantially different routing techniques. The performance of the routing algorithms depends on the difficulty of the problem instance, which is measured by a quantity lambda , known as the load factor. The pruned butterfly algorithm runs in time O( lambda log/sup 2/N), where N is the number of possible sources and destinations for messages and lambda is assumed to be polynomial in N. The sorting fat-free algorithm runs in O( lambda log N + log/sup 2/N) time for a restricted class of message sets, including partial permutations. Other results include a new type of sorting circuit, an area universal circuit, and an area-time lower bound for routers.<>
提出了两种确定性路由网络:修剪蝴蝶网络和排序胖树网络。这两个网络都是区域通用的，即它们可以模拟多对数减速，任何其他路由网络拟合在类似的区域。以前的区域通用网络要么是针对离线问题的，在离线问题中，要路由的消息集是事先已知的，并且允许进行大量的预计算，要么是涉及随机化，只能产生高概率的结果。目前的网络是第一个同时确定和在线的网络，它们使用两种完全不同的路由技术。路由算法的性能取决于问题实例的难易程度，难易程度由一个称为负载因子的量lambda来衡量。修剪蝴蝶算法的运行时间为O(lambda log/sup 2/N)，其中N是消息的可能源和目的地的数量，λ被假设为N中的多项式。对于受限的消息集(包括部分排列)，排序无脂肪算法的运行时间为O(lambda log N + log/sup 2/N)。其他成果还包括一种新型的排序电路、一种区域通用电路和路由器的区域时间下界。
{"title":"Deterministic on-line routing on area-universal networks","authors":"Paul Bay, G. Bilardi","doi":"10.1145/210346.210417","DOIUrl":"https://doi.org/10.1145/210346.210417","url":null,"abstract":"Two deterministic routing networks, the pruned butterfly and the sorting fat-tree, are presented. Both networks are area universal, i.e. they can simulate with polylogarithmic slowdown, any other routing network fitting in similar area. Previous area-universal networks were either for the offline problem, where the message set to be routed is known in advance and substantial precomputation is permitted, or involved randomization, yielding results that hold only with high probability. The present networks are the first that are simultaneously deterministic and online, and they use two substantially different routing techniques. The performance of the routing algorithms depends on the difficulty of the problem instance, which is measured by a quantity lambda , known as the load factor. The pruned butterfly algorithm runs in time O( lambda log/sup 2/N), where N is the number of possible sources and destinations for messages and lambda is assumed to be polynomial in N. The sorting fat-free algorithm runs in O( lambda log N + log/sup 2/N) time for a restricted class of message sets, including partial permutations. Other results include a new type of sorting circuit, an area universal circuit, and an area-time lower bound for routers.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"1 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":"130437158","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}
C. Kaklamanis, Anna R. Karlin, F. Leighton, V. Milenkovic, P. Raghavan, Satish Rao, C. Thomborson, A. Tsantilas
The computational power of 2-D and 3-D processor arrays that contain a potentially large number of faults is analyzed. Both a random and a worst-case fault model are considered, and it is proved that in either scenario low-dimensional arrays are surprisingly fault tolerant. It is also shown how to route, sort, and perform systolic algorithms for problems such as matrix multiplication in optimal time on faulty arrays. In many cases, the running time is the same as if there were no faults in the array (up to constant factors). On the negative side, it is shown that any constant congestion embedding of an n*n fault-free array on an n*n array with Theta (n/sup 2/) random faults (or Theta (log n) worst-case faults) requires dilation Theta (log n). For 3-D arrays, knot theory is used to prove that the required dilation is Omega ( square root log n).<>
{"title":"Asymptotically tight bounds for computing with faulty arrays of processors","authors":"C. Kaklamanis, Anna R. Karlin, F. Leighton, V. Milenkovic, P. Raghavan, Satish Rao, C. Thomborson, A. Tsantilas","doi":"10.1109/FSCS.1990.89547","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89547","url":null,"abstract":"The computational power of 2-D and 3-D processor arrays that contain a potentially large number of faults is analyzed. Both a random and a worst-case fault model are considered, and it is proved that in either scenario low-dimensional arrays are surprisingly fault tolerant. It is also shown how to route, sort, and perform systolic algorithms for problems such as matrix multiplication in optimal time on faulty arrays. In many cases, the running time is the same as if there were no faults in the array (up to constant factors). On the negative side, it is shown that any constant congestion embedding of an n*n fault-free array on an n*n array with Theta (n/sup 2/) random faults (or Theta (log n) worst-case faults) requires dilation Theta (log n). For 3-D arrays, knot theory is used to prove that the required dilation is Omega ( square root log n).<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"1 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":"128650775","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 time-space tradeoff is established in the branching program model for the problem of computing the product of two n*n matrices over a certain semiring. It is assumed that each element of each n*n input matrix is chosen independently to be 1 with probability n/sup -1/2/ and to be 0 with probability 1-n/sup -1/2/. Letting S and T denote expected space and time of a deterministic algorithm, the tradeoff is ST= Omega (n/sup 3.5/) for T0. The lower bounds are matched to within a logarithmic factor by upper bounds in the branching program model. Thus, the tradeoff possesses a sharp break at T= Theta (n/sup 2.5/). These expected case lower bounds are also the best known lower bounds for the worst case.<>
{"title":"A time-space tradeoff for Boolean matrix multiplication","authors":"Karl R. Abrahamson","doi":"10.1109/FSCS.1990.89561","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89561","url":null,"abstract":"A time-space tradeoff is established in the branching program model for the problem of computing the product of two n*n matrices over a certain semiring. It is assumed that each element of each n*n input matrix is chosen independently to be 1 with probability n/sup -1/2/ and to be 0 with probability 1-n/sup -1/2/. Letting S and T denote expected space and time of a deterministic algorithm, the tradeoff is ST= Omega (n/sup 3.5/) for T<c/sub 1/n/sup 2.5 /and ST Omega (n/sup 3/) for T<c/sub 2/n/sup 2.5/, where c/sub 1/,/sub /c/sub 2/ >0. The lower bounds are matched to within a logarithmic factor by upper bounds in the branching program model. Thus, the tradeoff possesses a sharp break at T= Theta (n/sup 2.5/). These expected case lower bounds are also the best known lower bounds for the worst case.<<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":"130341726","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 undirected, unweighted graph G=(V, E with n nodes, m edges, and connectivity lambda ) is considered. Given an input parameter delta , the edge augmentation problem is to find the smallest set of edges to add to G so that its edge-connectivity is increased by delta . A solution to this problem that runs in time O( delta /sup 2/nm+nF(n)), where F(n) is the time to perform one maximum flow on G, is given. The solution gives the optimal augmentation for every delta ', 1>
考虑无向无权图G=(V, E, n个节点，m条边，连通性λ)。给定一个输入参数delta，边缘增强问题是找到最小的边缘集来添加到G中，从而使其边缘连通性增加delta。这个问题的解决方案运行时间为O(δ /sup 2/nm+nF(n))，其中F(n)是在G上执行一次最大流量的时间。该解给出了每个δ '， 1>的最优增广。
{"title":"A fast algorithm for optimally increasing the edge-connectivity","authors":"D. Naor, D. Gusfield, C. Martel","doi":"10.1109/FSCS.1990.89592","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89592","url":null,"abstract":"An undirected, unweighted graph G=(V, E with n nodes, m edges, and connectivity lambda ) is considered. Given an input parameter delta , the edge augmentation problem is to find the smallest set of edges to add to G so that its edge-connectivity is increased by delta . A solution to this problem that runs in time O( delta /sup 2/nm+nF(n)), where F(n) is the time to perform one maximum flow on G, is given. The solution gives the optimal augmentation for every delta ', 1<or= delta '<or= delta , in the same time bound. A modification of the solution solves the problem without knowing delta in advance. If delta =1, then the solution is particularly simple, running in O(nm) time, and it is a natural generalization of an algorithm of K. Eswaran and R.E. Tarjan (1976) for the case in which lambda + delta =2. The converse problem (given an input number k, increase the connectivity of G as much as possible by adding at most k edges) is solved in the same time bound. The solution makes extensive use of the structure of particular sets of cuts.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"1 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":"131329882","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 determining the minimum number gamma of edges to be added to a graph G so that in the resulting graph the edge-connectivity between every pair (u,v) of nodes is at least a prescribed value r(u,v) is treated. A min-max formula for gamma is derived, and a polynomial-time algorithm for computing gamma is described. The directed counterpart of the problem is also solved for the case in which r(u,v)=k>or=1. The approach used makes it possible to solve a degree-constrained version of the problem. The minimum-cost augmentation problem can also be solved in polynomial time provided that the edge costs arise from node costs.<>
{"title":"Augmenting graphs to meet edge-connectivity requirements","authors":"A. Frank","doi":"10.1109/FSCS.1990.89593","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89593","url":null,"abstract":"The problem of determining the minimum number gamma of edges to be added to a graph G so that in the resulting graph the edge-connectivity between every pair (u,v) of nodes is at least a prescribed value r(u,v) is treated. A min-max formula for gamma is derived, and a polynomial-time algorithm for computing gamma is described. The directed counterpart of the problem is also solved for the case in which r(u,v)=k>or=1. The approach used makes it possible to solve a degree-constrained version of the problem. The minimum-cost augmentation problem can also be solved in polynomial time provided that the edge costs arise from node costs.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"147 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":"127256092","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 technique for enhancing the reliability of sorting networks and other comparator-based networks is presented. The technique converts any network that uses unreliable comparators to a fault-tolerant network that produces the correct output with overwhelming probability, even if each comparator is faulty with some probability smaller than 1/2, independently of other comparators. The depth of the fault-tolerant network is only a constant times the depth of the original network, and the width of the network is increased by a logarithmic factor.<>
{"title":"Fault tolerant sorting network","authors":"Shay Assaf, E. Upfal","doi":"10.1109/FSCS.1990.89546","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89546","url":null,"abstract":"A general technique for enhancing the reliability of sorting networks and other comparator-based networks is presented. The technique converts any network that uses unreliable comparators to a fault-tolerant network that produces the correct output with overwhelming probability, even if each comparator is faulty with some probability smaller than 1/2, independently of other comparators. The depth of the fault-tolerant network is only a constant times the depth of the original network, and the width of the network is increased by a logarithmic factor.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"7 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132571469","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 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 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}
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