Recently, Stanley [Longest alternating subsequences of permutations, preprint, arXiv/0511419v1] studied the length of the longest alternating subsequence of a permutation in the symmetric group,where a sequencea, b, c, d, . . . isalternating ifa >bd < · · ·. In this paper, we extend this result to the case of k-ary words. More precisely, we find an explicit formula for the generating functio...

The work of H. Hundal (Nonlinear Anal. 57 (2004), 35-61) has revealed that the sequence generated by the method of alternating projections converges weakly, but not strongly in general. This paper seeks to design strongly convergent algorithms by means of alternating the resolvents of two maximal monotone operators, A and B, that can be used to approximate common zeroes of A and B. In particula...

Let (A,λ) be a principally polarized abelian variety defined over a global field k, and let ∐∐(A) be its Shafarevich-Tate group. Let ∐∐(A)nd denote the quotient of ∐∐(A) by its maximal divisible subgroup. Cassels and Tate constructed a nondegenerate pairing ∐∐(A)nd ×∐∐(A)nd → Q/Z . If A is an elliptic curve, then by a result of Cassels the pairing is alternating. But in general it is only antis...

We prove: Theorem 0.1. Let K be a universal class. If K is categorical in cardinals of arbitrarily high cofinality, then K is categorical on a tail of cardinals. The proof stems from ideas of Adi Jarden and Will Boney, and also relies on a deep result of Shelah. As opposed to previous works, the argument is in ZFC and does not use the assumption of categoricity in a successor cardinal. The argu...

Abstract Geometrical Computation as a new model of computation is the counterpart of Cellular Automata that has Turing computing ability. In this paper we provide an algorithm to simulate Alternating Turing Machine in the context of Signal Machine using techniques adopted from the features of Signal Machine to set up and manage the copies/branches of Alternating Turing Machine. We show that our...

We consider abstraction in probabilistic process algebra. The process algebra can be employed for specifying processes that exhibit both probabilistic and non-deterministic choices in their behaviour. We give a set of axioms that completely axiomatises the branching bisimulation for the strictly alternating probabilistic graph model. In addition, several recursive verification rules are identif...

Timed Alternating Finite Automata (TAFA), a natural generalization of Timed Finite Automata (TFA), are synchronous and powerful models for real-time computations. They become an effective and expressive model for developing embedded systems with real-time constraint computations which are required in many applications. We introduce Deterministic Timed Alternating Finite Automata (DTAFA), a new ...

We show how alternating automata provide decision procedures for the equality of inductively de3ned Boolean functions and present applications to reasoning about parameterized families of circuits. We use alternating word automata to formalize families of linearly structured circuits and alternating tree automata to formalize families of tree structured circuits. We provide complexity bounds fo...

Variation in performances of an Information Retrieval system, which merges results from a number of retrieval schemes possessing equal and unequal weights, is studied in this paper. Weight of the retrieval schemes for a particular document is derived from the relevance scores of that corresponding document. Since, the relevance scores are varying from document to document and corpus to corpus, ...