N. Pippenger. On simultaneous resource bounds (preliminary version). In Proc. 20th IEEE Foundations of Computer Science, pages 307--311, 1979.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... back the origins of this thesis we come to a point where three rivers meet, two large ones and a smaller third one flowing like a meander around the second one: ffl Parallel algorithms ffl Formal languages ffl Natural languages The theory of parallel algorithms has been greatly influenced by [Bre74, Coo79, Pip79]. Sequential parsing has flourished by the need of good construction techniques for building compilers. Parsing theory is therefore mainly described in books on compiler design. Algorithms for natural languages, however, are often precursors of practical compiler algorithms [Ear68, Ear70, Hay62, ....

....isn t very realistic. A parallel algorithm is called feasible when it uses a polynomial number of processors. A parallel algorithm that is both fast and feasible, is called efficient. The class of problems with an efficient parallel algorithm is called Nick s Class NC (in honor of Nick Pippenger [Pip79]) It is an open question whether or not NC 6= P . Note that a feasible parallel algorithm running in polynomial time is called slow parallel, while the same algorithm performed by a single processor (in a round Robin fashion) is called fast (sequentially) Although we call an algorithm feasible ....

N. Pippenger. On simultaneous resource bounds. In 20 IEEE Symposium on Theory of Computing, pages 307--311, 1979.

....choices leads to a sink node with output value 1. A branching program of length d is leveled if the nodes can be partitioned into d sets V 0 , V 1 , V d where V 0 is the source, V d is the set of sink nodes and every arc out of V i goes to V i 1 , for 0 i d. It is well known[Pip79] that every branching program P of size s and length d, can be converted into a leveled branching program P # of length d that has at most s nodes in each of its levels and computes the same function as P (and is deterministic if P is) A branching program is oblivious if it is leveled and for ....

Nicholas J. Pippenger. On simultaneous resource bounds. In 20th Annual Symposium on Foundations of Computer Science, pages 307--311, San Juan, Puerto Rico, October 1979. IEEE.

....which is the length of the longest path. A branching program of length d is leveled if the nodes can be partitioned into d sets V 0 ; V 1 ; V d where V 0 = fstart B g is the source, V d is the set of sink nodes and every arc out of V i goes to V i 1 , for 0 i d. It is well known [Pip79] that every branching program B of size s and length d, can be converted into a leveled branching program B of length d that has at most s nodes in each of its levels and computes the same function as B (and is deterministic if P is) For our purposes, a randomized branching program e B with ....

Nicholas J. Pippenger. On simultaneous resource bounds. In 20th Annual Symposium on Foundations of Computer Science, pages 307--311, San Juan, Puerto Rico, October 1979. IEEE.

....2 logarithm of size. Any lower bound proven for a branching program also implies a lower bound for other computational models, such as Turing machines and Random Access Machines. A leveled branching program is a branching program in which the underlying graph is leveled. By a result of Pippenger [14], making a branching program leveled does not change T and adds at most log T to S. An oblivious branching program is a leveled branching program in which all the nodes on each level are labeled with the same variable. Call the sequence of variables reached at each level the query sequence of the ....

Nicholas J. Pippenger. On simultaneous resource bounds. In 20th Annual Symposium on Foundations of Computer Science, pages 307--311, San Juan, Puerto Rico, October 1979. IEEE.

....the connection to nonuniform and Boolean circuit complexity. By a result attributed to A. Meyer (cf. BH77] the class of languages that are polynomial time Turing reducible (i.e. by Cook reductions) to a sparse set is precisely the class of languages with polynomial size circuits. Pippenger [Pip79] showed that this is the same as the class P poly of languages that can be accepted with a polynomial amount of nonuniform advice. Thus sparse sets serve as a link between uniform complexity theory, which is based on the Turing machine model, and nonuniform complexity theory, which is based on ....

N. Pippenger. On simultaneous resource bounds. In Proc. 20th Annual IEEE Symposium on Foundations of Computer Science, pages 307--311, 1979.

....characterization of the class of sets with polynomial size circuits, i.e. a characterization of the class that does not directly use the notion of circuit or of circuit size. A set S is sparse if there is a polynomial p such that for all n 0, # x # S : 2 x # n # p(n) It is known [Pi79] that a set A has polynomial size circuits if and only if there is a sparse set set S such that A is polynomial time Turing reducible to S, i.e. A # P T S. This structural characterization of the sets with polynomial size circuits provides us with important information about the complexity of ....

N. Pippenger, On simultaneous resource bounds, in "Proc. 20th IEEE Sympos. Foundation of Comput. Sci.", IEEE (1979), 307-311.

....we have concentrated here on adjusting time complexities of algorithms described in [7] similar adjustments can be made to other work. An example is given in the following section. 6. 5 Analysis of the Boolean circuit model The authors of [61] claim real time simulation of the class NC 1 [63] in time proportional to the depth of the circuit. Recall that NC 1 defines the class of problems of size n solved by bounded fan in circuits of O(log n) depth and polynomial size. We point out that, with a single laboratory assistant, this estimate of the time complexity should be proportional ....

N. Pippenger. On simultaneous resource bounds. In 20th Annual Symposium on Foundations of Computer Science, pages 307--311, Long Beach, Ca., USA, October 1979. IEEE Computer Society Press.

....the length of a decision tree is referred to as its height. A branching program of length d is leveled if the nodes can be partitioned into d sets V 0 ; V 1 ; V d where V 0 is the source, V d is the set of sink nodes and every arc out of V i goes to V i 1 , for 0 i d. It is well known[Pip79] that every branching program P of size s and length d, can be converted into a leveled branching program P 0 of length d that has at most s nodes in each of its levels and computes the same function as P (and is deterministic if P is) 3 Decision Programs For a given Boolean function f , and ....

Nicholas J. Pippenger. On simultaneous resource bounds. In 20th Annual Symposium on Foundations of Computer Science, pages 307--311, San Juan, Puerto Rico, October 1979. IEEE.

....choices leads to a sink node with output value 1. A branching program of length d is leveled if the nodes can be partitioned into d sets V 0 , V 1 , V d where V 0 is the source, V d is the set of sink nodes and every arc out of V i goes to V i 1 , for 0 # i d. It is well known[Pip79] that every branching program P of size s and length d, can be converted into a leveled branching program P # of length d that has at most s nodes in each of its levels and computes the same function as P (and is deterministic if P is) 5 A branching program is oblivious if it is leveled and ....

Nicholas J. Pippenger. On simultaneous resource bounds. In 20th Annual Symposium on Foundations of Computer Science, pages 307--311, San Juan, Puerto Rico, October 1979. IEEE.

....complexity of a problem, one of the main questions they ask is whether a polylogarithmic running time is achievable on a PRAM containing a polynomial number of processors. If the answer is positive, then the problem and the corresponding algorithm are said to belong to class NC introduced in [22] (see also [8] 25] Having constructed an NC algorithm for a given problem, it is natural to try to improve its computational complexity. The complexity of a parallel algorithm is characterized by the pair (T ; P ) where T = T (N) is the worst case running time, P = P (N) is the number of ....

.... n) time 1 on graphs with bounded maximum degree. Unfortunately, when the degree is allowed to grow, the algorithms become inecient. The algorithm we present in this paper runs in O(log 4 n) time on an EREWPRAM consisting of O(m n) synchronous processors that share a common memory [8] [22], 25] 26] Each processor is a standard random access machine [2] capable of doing elementary operations on words of length O(log(n m) We follow the usual graph theoretic terminology [7] Our graphs are without loops or parallel edges. The vertices of a graph on n vertices are represented ....

N. Pippenger, On Simultaneous Resource Bounds, in Proc. 20th Annual IEEE Symposium on Foundations of Computer Science, 1979, pp. 307-311. M. GOLDBERG and T. SPENCER

....advice functions. Classes like P=poly are easily seen to be robust under allowing inputs x of length n in the given de nition, or even of length q(n) for some polynomial q ( 6] The hardware view of advice functions is supported by the following theorem that combines results of Pippenger [27], Yap [53] and Sch oning [35] Theorem 3. The following characterisations hold: i) P=poly is precisely the class of languages recognized by (possibly nonuniform) families of polynomial size circuits. ii) NP=poly is precisely the class of languages generated by (possibly on uniform) families ....

N. Pippenger. On simultaneous resource bounds, in: Proc. 20th Ann. IEEE Symp. Foundations of Computer Science (FOCS'79), 1979, pp. 307311.

....double bounded complexity classes by this quite dioeerent concept. Namely, we view the exponential time bounded languages in CSL, where CSL is the class of languages that can be recognized by a Turing machine in linear space. Little is known about such dual bounded classes; see, e.g. Coo79] [Pip79], B#r89] and [Rei90] Wolfgang Paul asks in general which kind of speedup theorem holds for spacebounded computations (see [Pau78] We concentrate on this question for the case of linear bounded automata. It is shown that this problem can be reformulated using our concept, which comes from ....

Nicholas Pippenger. On simultaneous resource bounds. In Proceedings of the 20th Annual Symposium on Foundations of Computer Science, Washington, D. C., 1979. Institute of Electrical and Electronics Engineers, IEEE Computer Society Press.

....[18] A typical model for nonuniform computations are circuit families. In the notation of Karp and Lipton [22] sets decidable by polynomial size circuits are precisely the sets in P poly; i.e. they are decidable in polynomial time with the help of a polynomial length bounded advice function [32]. Karp and Lipton (together with Sipser) 22] proved that no NP complete set has polynomial size circuits (in symbols NP ## P poly) unless the polynomial time hierarchy collapses to its second level. The proof given in [22] exploits a certain kind of self reducibility of the well known ....

N. Pippenger, On simultaneous resource bounds, in Proceedings of the 20th IEEE Symposium on the Foundations of Computer Science, IEEE Computer Society Press, Piscataway, NJ, 1979, pp. 307--311.

....a sparse p m complete set if and only if P = NP. The complexity of non uniform circuits is another field where sparse sets play a central role. The existence of sparse p T hard sets is investigated in this area. Meyer and Pippenger showed that the following classes coincide (see [BH77, Pip79] for definitions and proofs) Supported by the Studienstiftung des Deutschen Volkes. 1 P SPARSE the class of languages which are p T reducible to a sparse set P=poly the class of languages which are decidable in polynomial time using a polynomial advice SIZE(pol) the ....

N. Pippenger. On simultaneous resource bounds. In Proceedings of the 11th Annual ACM Symposium on the Theory of Computing, pages 307-311, 1979.

....and m edges the algorithm runs in time O(log 4 n) and uses O(n m) EREW PRAM processors. For graphs of constantly bounded valence, we can construct a maximal f matching in O(log n) time on an EREW PRAM with O(n) processors. 1. Introduction A problem belongs to the NC class introduced in [12] if it can be solved in poly logarithmic time on a PRAM with a polynomial number of processors. If we succeed in showing a problem to be in NC, the next step is to design an algorithm for the problem running in poly log time such that the product of the number of processors used by the algorithm ....

N. J. Pippenger, "On simultaneous resource bounds", Proc. 20th. Annual Symp. on Foundation of Computer Science, 1979, pp 307-311. 14

....a sequential algorithm that runs in O(w(n) time. Definition 1.1.3 An optimal parallel algorithm is an algorithm for which: w(n) O(T S (n) where T S (n) is the time expended by the fastest sequential algorithm for the problem. Definition 1.1. 4 A problem belongs to the class NC introduced in [39] if it can be solved by a PRAM algorithm in poly logarithmic time using a polynomial number of processors. That is, if T (n) and p(n) respectively stand for the time and the number of processors used by the algorithm then T (n) O(log k n) p(n) O(n ) for some integer constants k and ....

N. J. Pippenger, On simultaneous resource bounds. In the Proc. 20th. Annual Symp. on Foundation of Computer Science, 1979, pp 307-311.

....while simulating the circuit. Let A 2 NTIME SPACE(n O(1) log k ) be recognized by machine M whose input head sweeps back and forth across its input tape. It has been observed before that this is no loss of generality [PF79] Now a straightforward modi cation of an argument of Pippenger [Pip79] shows that A is accepted by a DLOGTIME uniform family of circuits fC n g of the following form: C n consists of O(n a log k n) gates arranged in n a levels, where gates at level i are either input gates or are connected to at most two gates at level i 1. 13 Each level i has O(log ....

N. Pippenger. On simultaneous resource bounds. In Proc. of 20th FOCS, pages 307-311, 1979.

....above results for the non preemptive scheduling of tasks are in contrast to a more positive set of results for preemptive scheduling. McNaughton [1959] produced a simple polynomial time algorithm and Martel [1988] shows that this version of the problem is in the complexity 17 class NC defined by Pippenger [1979]. In the case of preemptively scheduled tasks requiring more than one processor, Du and Leung [1989] show that the problem is ordinarily NP hard if processes require either one or k processors, and strongly NP hard if they are allowed to require an arbitrary number of processors. 6 Tasks with ....

Pippenger, N. (1979). On simultaneous resource bounds (preliminary version). In Proc. 20th IEEE FOCS, pages 307--311.

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N. Pippenger. On simultaneous resource bounds (preliminary version). In Proc. 20th IEEE Foundations of Computer Science, pages 307--311, 1979.

No context found.

N. Pippenger: "On simultaneous resource bounds", Proceedings of the 20-th IEEE Symposium on the Foundations of Computer Science, 1979, pp.307311.

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Nicholas J. Pippenger. On simultaneous resource bounds. In 20th Annual Symposium on Foundations of Computer Science, pages 307-311, San Juan, Puerto Rico, October 1979. IEEE.

No context found.

N. Pippenger: "On simultaneous resource bounds", Proceedings of the 20-th IEEE Symposium on the Foundations of Computer Science, 1979, pp.307-311.

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N. Pippenger. On simultaneous resource bounds. In Proc. of 20th FOCS, pages 307--311, 1979.

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Pippenger, N. (1979). On simultaneous resource bounds. Proc. of 20th Symposium on Foundations of Computer Science (FOCS), 307--311.

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N. Pippenger. On simultaneous resource bounds. In 20th Annual Symposium on Foundations of Computer Science, pages 307--311, San Juan, Puerto Rico, October 1979. IEEE.

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