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**1 - 4**of**4**### Progress in Computational Complexity Theory

"... We briefly survey a number of important recent achievements in Theoretical Computer Science (TCS), especially Computational Complexity Theory. We will discuss the PCP Theorem, its implications to inapproximability on combinatorial optimization problems; space bounded computations, especially determi ..."

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We briefly survey a number of important recent achievements in Theoretical Computer Science (TCS), especially Computational Complexity Theory. We will discuss the PCP Theorem, its implications to inapproximability on combinatorial optimization problems; space bounded computations, especially deterministic logspace algorithm for undirected graph connectivity problem; deterministic polynomial-time primality test; lattice complexity, worst-case to averagecase reductions; pseudorandomness and extractor constructions; and Valiant’s new theory of holographic algorithms and reductions.

### arXiv:math.NT/0502187 CONGRUENCES FOR SUMS OF BINOMIAL COEFFICIENTS

, 2005

"... Abstract. Let m> 0 and q> 1 be relatively prime integers. We find an explicit period νm(q) such that for any integers n � 0 and r we have n + νm(q) r ..."

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Abstract. Let m> 0 and q> 1 be relatively prime integers. We find an explicit period νm(q) such that for any integers n � 0 and r we have n + νm(q) r

### To appear in J. Number Theory. CONGRUENCES FOR SUMS OF BINOMIAL COEFFICIENTS

, 2007

"... Abstract. Let q> 1 and m> 0 be relatively prime integers. We find an explicit period νm(q) such that for any integers n> 0 and r we have h n + νm(q) i r ..."

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Abstract. Let q> 1 and m> 0 be relatively prime integers. We find an explicit period νm(q) such that for any integers n> 0 and r we have h n + νm(q) i r

### New version (2005-02-11), arXiv:math.NT/0502187. CONGRUENCES FOR SUMS OF BINOMIAL COEFFICIENTS

, 2005

"... Abstract. Let m> 0 and q> 1 be relatively prime integers. We find an explicit period νm(q) such that for any integers n � 0 and r we have n + νm(q) r ..."

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Abstract. Let m> 0 and q> 1 be relatively prime integers. We find an explicit period νm(q) such that for any integers n � 0 and r we have n + νm(q) r