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The NPcompleteness column: an ongoing guide
 JOURNAL OF ALGORITHMS
, 1987
"... 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. Freem ..."
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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
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 83 (6 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
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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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.
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 48 (7 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.
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 39 (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
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 34 (3 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...
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 31 (9 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 TimeSpace Complexity of Geometric Elimination Procedures
, 1999
"... In [25] and [22] a new algorithmic concept was introduced for the symbolic solution of a zero dimensional complete intersection polynomial equation system satisfying a certain generic smoothness condition. The main innovative point of this algorithmic concept consists in the introduction of a new ge ..."
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Cited by 29 (19 self)
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In [25] and [22] a new algorithmic concept was introduced for the symbolic solution of a zero dimensional complete intersection polynomial equation system satisfying a certain generic smoothness condition. The main innovative point of this algorithmic concept consists in the introduction of a new geometric invariant, called the degree of the input system, and the proof that the most common elimination problems have time complexity which is polynomial in this degree and the length of the input.