A propositional proof system can be viewed as a non-deterministic algorithm for the (co-NP complete) unsatisfiability problem. Many such proof systems, such as resolution, are also used as the basis for heuristics whi...
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ISBN:
(纸本)0897917855
A propositional proof system can be viewed as a non-deterministic algorithm for the (co-NP complete) unsatisfiability problem. Many such proof systems, such as resolution, are also used as the basis for heuristics which deterministically search for short proofs in the system. We discuss a propositional proof system based on algebraic reasoning, which we call the Groebner proof system because of a tight connection to the Groebner basis algorithm. For an appropriate measure of proof size, we show that (a degree-limited implementation of) the Groebner basis algorithm finds a Groebner proof of a tautology in time polynomial in the size of the smallest such proof, In other words, unlike most proof systems, the non-deterministic algorithm can be converted to a deterministic one without loss in power. We then compare the power of the Groebner proof system to more studied systems. We show that the Groebner system polynomially simulates Horn clause resolution, quasi-polynomially simulates tree-like resolution, and weakly exponentially simulates resolution. Thus, Groebner proofs will have better than worst-case behaviour on the same classes of inputs that resolution does. On the other hand, there are simple tautologies which have polynomialsize Groebner proofs but which require exponential-size resolution proofs. We also compare the Groebner proof system to the similar Nullstellensatz proof system introduced in [BIK+94]. We show a family of tautologies that have degree 3 (and hence polynomialsize) Groebner refutations, but which require Θ(√n) degree Nullstellensatz refutations. Thus, there is an exponential separation between the two systems. These results suggest that the Groebner basis algorithm might replace resolution as a basis for beuristics for NP-complate problems. We have done some preliminary experiments comparing [CW]'s implementation of the Groebner basis algorithm to [KS]'s implementation of the Putnam-Davis procedure for unsatisfiability. [KS]'s program is super
Distributed multimedia applications are a class of exciting new applications made possible by the emergence of highspeed networking and high-performance desktop computers. One important application in this class is de...
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The reliability of copper metallization on silicon-dioxide over single crystalline silicon was studied by capacitance techniques, secondary-ion-mass spectroscopy analysis and Rutherford Back Scattering. The metallizat...
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The spectral/power efficiency and performance of the pi /4-quadrature phase-shift keying (QPSK) modems (American and Japanese digital cellular emerging standards) are studied and briefly compared to GMSK modems (propo...
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The spectral/power efficiency and performance of the pi /4-quadrature phase-shift keying (QPSK) modems (American and Japanese digital cellular emerging standards) are studied and briefly compared to GMSK modems (proposed for European Digital European Cordless Telephone System) (DECT) and Group Special Mobile System (GSM) cellular standards). Improved filtering strategies and digital pilot aided (digital channel sounding) techniques are considered for pi /4-QPSK and for other digital modems. More spectrally efficient modem trends and some research results for future cellular/mobile (land mobile) and satellite communication systems applications are also highlighted.< >
Bias dependence of the drain current noise power of SOI MOSFET's were studied and low frequency noise overshoot at the drain current kink is observed for the first time in SOI MOSFET. The overshoot has a width of ...
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We show that the several problems, whose complexity with respect P and NC was open, are equivalent under NC-reductions. These include: (1) Finding the optimal solution of a two-variable integer program;(2) Determining...
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This paper describes an improved method for evaluating disk cache performance using trace driven simulation. This method differentiates between reads and writes in the trace data which results in higher miss ratios th...
ISBN:
(纸本)0818608455
This paper describes an improved method for evaluating disk cache performance using trace driven simulation. This method differentiates between reads and writes in the trace data which results in higher miss ratios than when all traced events are treated alike. It allows for simulating various update policies and update intervals, physical blocks that are part of different files at different times, and the optimum replacement policy GOPT. These methods are applied to traces from a VAX 11/780 running 4.3 BSD UNIX to illustrate the importance of including writes in the traces and also to analyze the effects of choosing various update intervals.
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