We define deterministic arithmetic automata (DAAs) and connect them to a framework called probabilistic arithmetic automata (PAAs) [9]. We use DAAs and PAAs to compute the entire exact probability distribution (in contrast to, e.g., asymptotic expectation and variance) of the number X of text characters accessed by the Horspool or Sunday pattern matching algorithms when matching a fixed pattern...

A topological space has calibre ω1 (resp., calibre (ω1,ω)) if every point-countable (resp., point-finite) collection of nonempty open sets is countable. It has compact-calibre ω1 (resp., compact-calibre (ω1,ω)) if, for every family of uncountably many nonempty open sets, there is some compact set which meets uncountably many (resp., infinitely many) of them. It has CCC (resp., DCCC) if every di...

The Boyer-Moore algorithm uses two pre-computed tables for searching a string: skip, which utilizes the occurrence heuristic of symbols in a pattern, and shift, which utilizes the match heuristic of the pattern. Researchers have pointed out that the difficulty of understanding the computation of the shift table has hindered utilization of the algorithm in a wider range of applications. This pap...

We characterize the tempered part of automorphic Langlands category D-mod(Bun_G) using geometry big cell in affine Grassmannian. deduce that, for $G$ non-abelian, D-modules have no de Rham cohomology with compact supports. The latter fact boils down to a concrete statement, which we prove Ran space and some explicit t-structure estimates: non-abelian $\Sigma$ smooth curve, Borel-Moore homology ...

There are two distinct approaches to solving reinforcement learning problems, namely, searching in value function space and searching in policy space. Temporal diierence methods and evolutionary algorithms are well-known examples of these approaches. Kaelbling, Littman and Moore recently provided an informative survey of temporal diierence methods. This article focuses on the application of evo...

Profinite equations are an indispensable tool for the algebraic classification of formal languages. Reiterman’s theorem states that they precisely specify pseudovarieties, i.e., classes finite algebras closed under products, subalgebras and quotients. In this article, is generalized to Eilenberg-Moore a monad T on category D: we prove class -algebras pseudovariety iff it presentable by profinit...

We prove here a well known result in graph theory, originally proved by Hoffman and Singleton, that any non-trivial Moore graph of diameter 2 is regular of degree k = 2, 3, 7 or 57. The existence (and uniqueness) of these graphs is known for k = 2, 3, 7 while it is still an open problem if there is a moore graph of degree 57 or not.

In this paper, the notion of Moore–Penrose biorthogonal systems is generalized. In [Fiedler, Moore–Penrose biorthogonal systems in Euclidean spaces, Lin. Alg. Appl. 362 (2003), pp. 137–143], transformations of generating systems of Euclidean spaces are examined in connection with the Moore-Penrose inverses of their Gram matrices. In this paper, g-inverses are used instead of the Moore–Penrose i...