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We describe a new quantifier elimination algorithm for real closed fields based on Thom encoding and sign determination. The complexity of this algorithm is elementary recursive and its proof of correctness is completely algebraic. In particular, the notion of connected components of semialgebraic sets is not used. [ABSTRACT FROM AUTHOR]

Abstract: An improved algorithm, together with its implementation, is presented for the automatic computation of the complete root classification of a real parametric polynomial. The algorithm offers improved efficiency and a new test for non-realizable conditions. The improvement lies in the direct use of ‘sign lists’, obtained from the discriminant sequence, rather than ‘revised sign lists’. It is shown that the discriminant sequences, upon which the sign lists are based, are closely related both to Sturm–Habicht sequences and to subresultant sequences. Thus calculations based on any of these quantities are essentially equivalent. One particular application of complete root classifications is the determination of the conditions for the positive definiteness of a polynomial, and here the new algorithm is applied to a class of sparse polynomials. It is seen that the number of conditions for positive definiteness remains surprisingly small in these cases. [Copyright &y& Elsevier]

Abstract: We first look at an existing infinitary sequent system for common knowledge for which there is no known syntactic cut-elimination procedure and also no known non-trivial bound on the proof-depth. We then present another infinitary sequent system based on nested sequents that are essentially trees and with inference rules that apply deeply inside these trees. Thus we call this system “deep” while we call the former system “shallow”. In contrast to the shallow system, the deep system allows one to give a straightforward syntactic cut-elimination procedure. Since both systems can be embedded into each other, this also yields a syntactic cut-elimination procedure for the shallow system. For both systems we thus obtain an upper bound of on the depth of proofs, where is the Veblen function. [Copyright &y& Elsevier]

Abstract: This paper proves the strong normalization of classical natural deduction with disjunction and permutative conversions, by using CPS-translation and augmentations. Using them, this paper also proves the strong normalization of classical natural deduction with general elimination rules for implication and conjunction, and their permutative conversions. This paper also proves that natural deduction can be embedded into natural deduction with general elimination rules, strictly preserving proof normalization. [Copyright &y& Elsevier]

Abstract: A simple cut elimination proof for arithmetic with the epsilon symbol is used to establish the termination of a modified epsilon substitution process. This opens a possibility of extension to much stronger systems. [Copyright &y& Elsevier]

Abstract: For a tree T and an integer , it is well known that the kth power of T is strongly chordal and hence has a strong elimination ordering of its vertices. In this note we obtain a complete characterization of strongly simplicial vertices of , thereby characterizing all strong elimination orderings of the vertices of . [Copyright &y& Elsevier]

Abstract: We present a Gröbner basis associated with the symmetric group of degree , which is determined by a strong generating set of the symmetric group and is defined by means of a term ordering with the elimination property. [Copyright &y& Elsevier]

Abstract: We introduce a system of simply typed lambda terms (with fixed point combinators) and show that a rather comprehensive class of (co-)recursion equations on streams or non-wellfounded trees can be solved in our system. Moreover certain conditions are presented which guarantee that the defined functionals are primitive recursive. As a major example we give a co-recursive treatment of Mints’ continuous cut-elimination operator. [Copyright &y& Elsevier]

Abstract: We give geometric axioms for existentially closed Hasse fields. We prove a quantifier elimination result for existentially closed -truncated Hasse fields and characterize them as reducts of existentially closed Hasse fields. [Copyright &y& Elsevier]

This paper proposes an unambiguous correlation function applicable to generic sine-phased binary offset carrier (BOC) signal tracking. In the proposed scheme, first, we view the BOC sub-carrier pulse as a sum of multiple rectangular pulses. Then, we obtain partial correlation functions by correlating the multiple rectangular pulses with the received signal, and subsequently, construct two symmetric correlation functions by combining the partial correlation functions in a specialized way. Finally, we generate an unambiguous correlation function by combining the two symmetric correlation functions. The proposed correlation function has a sharper main-peak, and consequently, provides a better tracking performance than those of the conventional correlation functions in terms of the tracking error standard deviation (TESD). [ABSTRACT FROM AUTHOR]

A constant scoring rule asks each individual to vote for a given (and constant) number of alternatives and the alternative with the most votes is elected. A sequential constant scoring rule applies this principle in a process of sequential elimination. Constant scoring rules as well as sequential constant scoring rules fail to satisfy Condorcet criteria when individual preferences are unrestricted. The purpose of this paper is to show that, if we assume that preferences are single-peaked, then some constant scoring rules satisfy the Condorcet loser criterion and some sequential constant scoring rules satisfy the Condorcet winner criterion. The results we provide make possible the identification of these rules. [ABSTRACT FROM AUTHOR]

Abstract: A real matrix A, of size , is called totally nonnegative (totally positive) if all its minors are nonnegative (positive). A variant of the Neville elimination process is studied in relation to the existence of a totally nonnegative elementary bidiagonal factorization of A. The class of quasi- oscillatory rectangular matrices, which in the square case contains the oscillatory matrices, is introduced and a characterization of this class of matrices, by incorporating bidiagonal factorization, is showed. [Copyright &y& Elsevier]

Abstract: We consider the use of state elimination to construct shorter regular expressions from finite-state automata (FAs). Although state elimination is an intuitive method for computing regular expressions from FAs, the resulting regular expressions are often very long and complicated. We examine the minimization of FAs to obtain shorter expressions first. Then, we introduce vertical chopping based on bridge states and horizontal chopping based on the structural properties of given FAs. We prove that we should not eliminate bridge states until we eliminate all non-bridge states to obtain shorter regular expressions. In addition, we suggest heuristics for state elimination that leads to shorter regular expressions based on vertical chopping and horizontal chopping. [Copyright &y& Elsevier]