It is shown that disjunction of two switch-lists can blow up the representation size exponentially. Since switch-lists can be negated without any increase in size, this shows that conjunction of switch-lists also leads to an exponential blow-up in general.
We investigate the NP-Complete problem SAT and the geometry of its instances. For a particular type that we call {\it non-interlaced formulas}, we propose a polynomial time algorithm for their resolution using graphs and matrices.
Consider the problem of finding a point in a metric space $(\{1,2,\ldots,n\},d)$ with the minimum average distance to other points. We show that this problem has no deterministic $o(n^{1+1/(h-1)})$-query $(2h-Ω(1))$-approximation algorithms for any constant $h\in\mathbb{Z}^+\setminus\{1\}$.
We use existential Diophantine predicates carefully reinterpreted over the reals and the time complexity of Tarski algebra to show that 3-CNF SAT is in n^O(log^{gamma} n) time for an absolute positive constant gamma.
This survey describes, at an introductory level, the algebraic complexity framework originally proposed by Leslie Valiant in 1979, and some of the insights that have been obtained more recently.
We prove that for sufficiently large K, it is NP-hard to color K-colorable graphs with less than 2^{K^{1/3}} colors. This improves the previous result of K versus K^{O(log K)} in Khot [14].
Bauwens, Mahklin, Vereshchagin and Zimand [ECCC TR13-007] and Teutsch [arxiv:1212.6104] have shown that given a string x it is possible to construct in polynomial time a list containing a short description of it. We simplify their technique and present a shorter proof of this result.
Solving an open problem stated by Shvachko, it is shown that a language which is not real-time recognizable by some variants of pointer machines can be accepted by a Kolmogorov-Uspensky machine in real-time.
Oral Diseases 17, 564–571Objective: WWOX gene is altered in a variety of neoplasms. Wwox is pro‐apoptotic through interaction with p73 and may be involved in chromosomal stability by interaction with p73 and p53. The aims of this study were to characterize WWOX transcription, methylation status and immunoexpression in salivary neoplasms and to determine whether these were associated with p73, p53, cell proliferation and DNA ploidy.Materials and Methods: Seven malignant and 21 benign fresh salivary neoplasms were included. WWOX expression was determined by RT‐PCR and sequencing of transcripts, quantitative PCR and immunohistochemistry. Methylation‐specific PCR was used to assess the methylation of its first exon. For p73, ΔNp73, p53 and ki67 immunohistochemistry and ploidy analysis, 29 malignant samples from archives were included.Results: No consistent pattern of WWOX exon 1 methylation was found, but aberrant and novel transcripts were observed in 17/28 neoplasms; 55% of tumours showed reduced WWOX RNA. WWOX RNA levels were associated with p53 immunopositivity. Immunohistochemical Wwox expression did not correlate with methylation status, p53 or p73 expression or proliferation. p73, proliferation and DNA ploidy were associated with malignant phenotype.Conclusion: Aberrant WWOX transcription and decreased expression are frequent in salivary neoplasms and WWOX transcription is associated with p53 staining.
There are errors in the algorithm proposed by Narendra Chaudhari [2] purporting to solve the 3-sat problem in polynomial time. The present paper present instances for which the algorithm outputs erroneous results.
0-1 Knapsack is a fundamental NP-complete problem. In this article we prove that it remains NP-complete even when the weights of the objects in the packing constraints and their values in the objective function satisfy specific stringent conditions: the values are integral powers of the weights of the objects.