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79
The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co ..."
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Cited by 188 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
The Boolean formula value problem is in ALOGTIME
 in Proceedings of the 19th Annual ACM Symposium on Theory of Computing
, 1987
"... The Boolean formula value problem is in alternating log time and, more generally, parenthesis contextfree languages are in alternating log time. The evaluation of reverse Polish notation Boolean formulas is also in alternating log time. These results are optimal since the Boolean formula value ..."
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Cited by 66 (7 self)
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The Boolean formula value problem is in alternating log time and, more generally, parenthesis contextfree languages are in alternating log time. The evaluation of reverse Polish notation Boolean formulas is also in alternating log time. These results are optimal since the Boolean formula value problem is complete for alternating log time under deterministic log time reductions. Consequently, it is also complete for alternating log time under AC reductions.
Models of Computation  Exploring the Power of Computing
"... Theoretical computer science treats any computational subject for which a good model can be created. Research on formal models of computation was initiated in the 1930s and 1940s by Turing, Post, Kleene, Church, and others. In the 1950s and 1960s programming languages, language translators, and oper ..."
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Cited by 57 (7 self)
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Theoretical computer science treats any computational subject for which a good model can be created. Research on formal models of computation was initiated in the 1930s and 1940s by Turing, Post, Kleene, Church, and others. In the 1950s and 1960s programming languages, language translators, and operating systems were under development and therefore became both the subject and basis for a great deal of theoretical work. The power of computers of this period was limited by slow processors and small amounts of memory, and thus theories (models, algorithms, and analysis) were developed to explore the efficient use of computers as well as the inherent complexity of problems. The former subject is known today as algorithms and data structures, the latter computational complexity. The focus of theoretical computer scientists in the 1960s on languages is reflected in the first textbook on the subject, Formal Languages and Their Relation to Automata by John Hopcroft and Jeffrey Ullman. This influential book led to the creation of many languagecentered theoretical computer science courses; many introductory theory courses today continue to reflect the content of this book and the interests of theoreticians of the 1960s and early 1970s. Although
An Optimal Parallel Algorithm for Formula Evaluation
, 1992
"... A new approach to Buss’s NC¹ algorithm [Proc. 19thACM Symposium on Theory of Computing, Association for Computing Machinery, New York, 1987, pp. 123131] for evaluation of Boolean formulas is presented. This problem is shown to be complete for NC¹ over AC¬ reductions. This approach is then used to s ..."
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Cited by 43 (6 self)
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A new approach to Buss’s NC¹ algorithm [Proc. 19thACM Symposium on Theory of Computing, Association for Computing Machinery, New York, 1987, pp. 123131] for evaluation of Boolean formulas is presented. This problem is shown to be complete for NC¹ over AC¬ reductions. This approach is then used to solve the more general problem of evaluating arithmetic formulas by using arithmetic circuits.
The Complexity of Computation on the Parallel Random Access Machine
, 1993
"... PRAMs also approximate the situation where communication to and from shared memory is much more expensive than local operations, for example, where each processor is located on a separate chip and access to shared memory is through a combining network. Not surprisingly, abstract PRAMs can be much m ..."
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Cited by 32 (4 self)
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PRAMs also approximate the situation where communication to and from shared memory is much more expensive than local operations, for example, where each processor is located on a separate chip and access to shared memory is through a combining network. Not surprisingly, abstract PRAMs can be much more powerful than restricted instruction set PRAMs. THEOREM 21.16 Any function of n variables can be computed by an abstract EROW PRAM in O(log n) steps using n= log 2 n processors and n=2 log 2 n shared memory cells. PROOF Each processor begins by reading log 2 n input values and combining them into one large value. The information known by processors are combined in a binarytreelike fashion. In each round, the remaining processors are grouped into pairs. In each pair, one processor communicates the information it knows about the input to the other processor and then leaves the computation. After dlog 2 ne rounds, one processor knows all n input values. Then this processor computes th...
Limits on the Power of Quantum Statistical ZeroKnowledge
, 2003
"... In this paper we propose a definition for honest verifier quantum statistical zeroknowledge interactive proof systems and study the resulting complexity class, which we denote QSZK ..."
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Cited by 30 (4 self)
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In this paper we propose a definition for honest verifier quantum statistical zeroknowledge interactive proof systems and study the resulting complexity class, which we denote QSZK
Randomized and Deterministic Algorithms for the Dimension of Algebraic Varieties
 In Proc. 38th IEEE Symposium on Foundations of Computer Science
, 1997
"... We prove old and new results on the complexity of computing the dimension of algebraic varieties. In particular, we show that this problem is NPcomplete in the BlumShubSmale model of computation over C , that it admits a s O(1) D O(n) deterministic algorithm, and that for systems with integer ..."
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Cited by 25 (9 self)
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We prove old and new results on the complexity of computing the dimension of algebraic varieties. In particular, we show that this problem is NPcomplete in the BlumShubSmale model of computation over C , that it admits a s O(1) D O(n) deterministic algorithm, and that for systems with integer coefficients it is in the ArthurMerlin class under the Generalized Riemann Hypothesis. The first two results are based on a general derandomization argument. 1 Introduction We wish to compute the dimension of an algebraic variety V ` C n defined by a system of algebraic equations f 1 (x) = 0; : : : ; f s (x) = 0 (1) where f i 2 C [X 1 ; : : : ; Xn ]. This can be formalized as a decision problem DIMC . An instance of DIMC is a system of this form together with an integer d n. An instance is accepted if the variety defined by the system has dimension at least d. We also consider for each fixed value of d the restriction DIM d C of DIMC . For instance, DIM 0 C is the problem of dec...
A Uniform Circuit Lower Bound for the Permanent
 SIAM Journal on Computing
, 1994
"... We show that uniform families of ACC circuits of subexponential size cannot compute the permanent function. This also implies similar lower bounds for certain sets in PP. This is one of the very few examples of a lower bound in circuit complexity whose proof hinges on the uniformity condition; it is ..."
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Cited by 24 (10 self)
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We show that uniform families of ACC circuits of subexponential size cannot compute the permanent function. This also implies similar lower bounds for certain sets in PP. This is one of the very few examples of a lower bound in circuit complexity whose proof hinges on the uniformity condition; it is still unknown if there is any set in Ntime #2 n O#1# # that does not have nonuniform ACC circuits.
On the power of real Turing machines over binary inputs
 SIAM Journal on Computing
, 1997
"... this paper is to prove that BP(PAR IR ) = PSPACE/poly where PAR IR is the class of sets computed in parallel polynomial time by (ordinary) real Turing machines. As a consequence we obtain the existence of binary sets that do not belong to the Boolean part of PAR IR (an extension of the result in [20 ..."
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Cited by 24 (3 self)
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this paper is to prove that BP(PAR IR ) = PSPACE/poly where PAR IR is the class of sets computed in parallel polynomial time by (ordinary) real Turing machines. As a consequence we obtain the existence of binary sets that do not belong to the Boolean part of PAR IR (an extension of the result in [20] since PH IR ` PAR IR ) and a separation of complexity classes in the real setting.