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A morphic approach to combinatorial games : the Tribonacci case

Eric Duchêne, Michel Rigo (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We propose a variation of Wythoff’s game on three piles of tokens, in the sense that the losing positions can be derived from the Tribonacci word instead of the Fibonacci word for the two piles game. Thanks to the corresponding exotic numeration system built on the Tribonacci sequence, deciding whether a game position is losing or not can be computed in polynomial time.

A morphic approach to combinatorial games: the Tribonacci case

Eric Duchêne, Michel Rigo (2007)

RAIRO - Theoretical Informatics and Applications

We propose a variation of Wythoff's game on three piles of tokens, in the sense that the losing positions can be derived from the Tribonacci word instead of the Fibonacci word for the two piles game. Thanks to the corresponding exotic numeration system built on the Tribonacci sequence, deciding whether a game position is losing or not can be computed in polynomial time.

A new algebraic invariant for weak equivalence of sofic subshifts

Laura Chaubard, Alfredo Costa (2008)

RAIRO - Theoretical Informatics and Applications

It is studied how taking the inverse image by a sliding block code affects the syntactic semigroup of a sofic subshift. The main tool are ζ-semigroups, considered as recognition structures for sofic subshifts. A new algebraic invariant is obtained for weak equivalence of sofic subshifts, by determining which classes of sofic subshifts naturally defined by pseudovarieties of finite semigroups are closed under weak equivalence. Among such classes are the classes of almost finite type subshifts...

A new curve fitting based rating prediction algorithm for recommender systems

Yilmaz Ar, Şahin Emrah Amrahov, Nizami A. Gasilov, Sevgi Yigit-Sert (2022)

Kybernetika

The most algorithms for Recommender Systems (RSs) are based on a Collaborative Filtering (CF) approach, in particular on the Probabilistic Matrix Factorization (PMF) method. It is known that the PMF method is quite successful for the rating prediction. In this study, we consider the problem of rating prediction in RSs. We propose a new algorithm which is also in the CF framework; however, it is completely different from the PMF-based algorithms. There are studies in the literature that can increase...

A new practical linear space algorithm for the longest common subsequence problem

Heiko Goeman, Michael Clausen (2002)

Kybernetika

This paper deals with a new practical method for solving the longest common subsequence (LCS) problem. Given two strings of lengths m and n , n m , on an alphabet of size s , we first present an algorithm which determines the length p of an LCS in O ( n s + min { m p , p ( n - p ) } ) time and O ( n s ) space. This result has been achieved before [ric94,ric95], but our algorithm is significantly faster than previous methods. We also provide a second algorithm which generates an LCS in O ( n s + min { m p , m log m + p ( n - p ) } ) time while preserving the linear space bound, thus solving...

A non-uniform finitary relational semantics of system T

Lionel Vaux (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We study iteration and recursion operators in the denotational semantics of typed λ-calculi derived from the multiset relational model of linear logic. Although these operators are defined as fixpoints of typed functionals, we prove them finitary in the sense of Ehrhard’s finiteness spaces.

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