In this paper, we describe a general method for building coverings, that we call lexicographic covering. The name comes from the fact that the scheme although more general than that is particularly fitted to the case where the transitions of an automaton are given an ordering at each state and thus the computations in the automaton may be lexicographic ordered. The lexicographic covering allows...

The purpose of this paper is to learn the order of criteria of lexicographic decision under various reasonable assumptions. We give a sample evaluation and an oracle based algorithm. In the worst case analysis we are dealing with the adversarial models. We show that if the distances of the samples are less than 4, then it is not learnable, but 4-distance samples are polynomial learnable.

A linear ordering (X,≺) is a Debreu chain (or has the Debreu property) if each subordering (Y,≺) of X can be embedded into X with an injective function that is both order-preserving and continuous with respect to the order topology on X and Y . The most typical example of a Debreu chain is the linearly ordered topological space (R, <, τ<) of real numbers endowed with its usual order < and the o...

In Tversky’s (1969) model of a lexicographic semiorder, a preference is generated via the sequential application of numerical criteria by declaring an alternative x better than an alternative y if the first criterion that distinguishes between x and y ranks x higher than y by an amount exceeding a fixed threshold. We generalize this idea to a fully fledged model of boundedly rational choice. We...

Considering the smallest and the greatest factorswith respect to the lexicographic orderwe associate to each infinite word r two other infinite words min(r) and max(r). In this paper we prove that the inequalities as min(s) max(s) bs characterize standard Sturmian words (proper ones and periodic ones) and that the condition “for any x ∈ A and lexicographic order< satisfying x=min(A) one has xs ...

This paper is aimed at studying the Time Minimizing Transportation Problem with Fractional Bottleneck Objective Function (TMTP-FBOF). TMTP-FBOF is related to a Lexicographic Fractional Time Minimizing Transportation Problem (LFTMTP), which will be solved by a lexicographic primal code. An algorithm is also developed to determine an initial efficient basic solution to this TMTP-FBOF. The develop...

It is shown that a termination proof for a term rewriting system using a lexicographic path ordering yields a multiply recursive bound on the length of derivations, measured in the depth of the starting term. This result is essentially optimal since for every multiply recursive function f a rewrite system (which reduces under the lexicographic path ordering) can be found such that its derivatio...

We study the degree of polynomial representations of knots. We obtain the lexicographic degree for two-bridge torus knots and generalized twist knots. The proof uses the braid theoretical method developed by Orevkov to study real plane curves, combined with previous results from [KP10] and [BKP14]. We also give a sharp lower bound for the lexicographic degree of any knot, using real polynomial ...

We present uniform and non-uniform algorithms to rank and unrank permutations in lexicographic order. The uniform algorithms run in O(n log n) time and outperform Knuth’s ranking algorithm in all the experiments, and also the lineartime non-lexicographic algorithm of Myrvold-Ruskey for permutations up to size 128. The non-uniform algorithms generalize Korf-Schultze’s linear time algorithm yet r...

We consider voting over combinatorial domains, where alternatives are binary tuples. We assume that votes are specified as conditionally lexicographic preferences, or LP trees. We study aggregation problems of LP tree votes for several positional scoring rules. Our main goal is to demonstrate that answer-set programming can be effective in solving the winner and the evaluation problems for inst...