Related papers: Deciding Conjugacy of a Rational Relation

Let A be a class of objects, equipped with an integer size such that for all n the number a(n) of objects of size n is finite. We are interested in the case where the generating fucntion sum_n a(n) t^n is rational, or more generally…

This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and…

We introduce a novel choice dataset, called joint choice, in which options and menus are multidimensional. In this general setting, we define a notion of choice separability, which requires that selections from some dimensions are never…

We give a reciprocity formula for a two-variable sum where the variables satisfy a linear congruence condition. We also prove that such sum is a measure of how well a rational is approximable from below and show that the reciprocity formula…

We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…

Let G be a word-hyperbolic group with given finite generating set, for which various standard structures and constants have been pre-computed. A (non-practical) algorithm is described that, given as input two lists A and B, each composed of…

Automatic evaluation of semantic rationality is an important yet challenging task, and current automatic techniques cannot well identify whether a sentence is semantically rational. The methods based on the language model do not measure the…

Let G be a finite group. An element x in G is a real element if x is conjugate to its inverse in G. For x in G, the conjugacy class x^G is said to be a real conjugacy class if every element of x^G is real. We show that if 4 divides no real…

An automaton is history-deterministic if its nondeterminism can be resolved on the fly, only using the prefix of the word read so far. This mild form of nondeterminism has attracted particular attention for its applications in synthesis…

The relational calculus (RC) is a concise, declarative query language. However, existing RC query evaluation approaches are inefficient and often deviate from established algorithms based on finite tables used in database management…

Conversational implicatures are usually described as being licensed by the disobeying or flouting of a Principle of Cooperation. However, the specification of this principle has proved computationally elusive. In this paper we suggest that…

In this paper, we focus on the problem of determining whether two conjunctive ("CQ") queries posed on relational data are combined-semantics equivalent [9]. We continue the tradition of [2,5,9] of studying this problem using the tool of…

The study of verbal subgroups within a group is well-known for being an effective tool to obtain structural information about a group. Therefore, conditions that allow the classification of words in a free group are of paramount importance.…

Probabilistic separation logic offers an approach to reasoning about imperative probabilistic programs in which a separating conjunction is used as a mechanism for expressing independence properties. Crucial to the effectiveness of the…

In the context of strategic games, we provide an axiomatic proof of the statement Common knowledge of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies.…

The natural join and the inner union operations combine relations of a database. Tropashko and Spight [24] realized that these two operations are the meet and join operations in a class of lattices, known by now as the relational lattices.…

Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…

Relation-changing modal logics are extensions of the basic modal logic that allow changes to the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to…

In relational verification, judicious alignment of computational steps facilitates proof of relations between programs using simple relational assertions. Relational Hoare logics (RHL) provide compositional rules that embody various…

We show that the first-order logical theory of the binary overlap-free words (and, more generally, the ${\alpha}$-free words for rational ${\alpha}$, $2 < {\alpha} \leq 7/3$), is decidable. As a consequence, many results previously obtained…