Related papers: Arithmetic Expression Construction
This work presents code to procedurally generate examples for the ARC training tasks. For each of the 400 tasks, an example generator following the transformation logic of the original examples was created. In effect, the assumed underlying…
In formal languages and automata theory, the magic number problem can be formulated as follows: for a given integer n, is it possible to find a number d in the range [n,2^n] such that there is no minimal deterministic finite automaton with…
In this paper, we study $k$-term arithmetic progressions $N, N+d, ..., N+(k-1)d$ of powerful numbers. Under the $abc$-conjecture, we obtain $d \gg_\epsilon N^{1/2 - \epsilon}$. On the other hand, there exist infinitely many $3$-term…
The recent approaches of extending the GRAPHPLAN algorithm to handle more expressive planning formalisms raise the question of what the formal meaning of "expressive power" is. We formalize the intuition that expressive power is a measure…
In this paper, we focus our attention on the interval temporal logic of the Allen's relations "meets", "begins", and "begun by" (ABBar for short), interpreted over natural numbers. We first introduce the logic and we show that it is…
Some classical graph problems such as finding minimal spanning tree, shortest path or maximal flow can be done efficiently. We describe slight variations of such problems which are shown to be NP-complete. Our proofs use straightforward…
Applications such as employees sharing office spaces over a workweek can be modeled as problems where agents are matched to resources over multiple rounds. Agents' requirements limit the set of compatible resources and the rounds in which…
Interval arithmetic is a simple way to compute a mathematical expression to an arbitrary accuracy, widely used for verifying floating-point computations. Yet this simplicity belies challenges. Some inputs violate preconditions or cause…
The interval numbers is the set of compact intervals of $\mathbb{R}$ with addition and multiplication operation, which are very useful for solving calculations where there are intervals of error or uncertainty, however, it lacks an…
The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment to contexts involving relations of arity greater than two. Quantifiers in this logic are used in…
We show NP-completeness for several planar variants of the monotone satisfiability problem with bounded variable appearances. With one exception the presented variants have an associated bipartite graph where the vertex degree is bounded by…
This study introduces a procedure to obtain general expressions, $y = f(x)$, subject to linear constraints on the function and its derivatives defined at specified values. These constrained expressions can be used describe functions with…
Timed regular expressions serve as a formalism for specifying real-time behaviors of Cyber-Physical Systems. In this paper, we consider the synthesis of timed regular expressions, focusing on generating a timed regular expression consistent…
We study a new formulation of the team-formation problem, where the goal is to form teams to work on a given set of tasks requiring different skills. Deviating from the classic problem setting where one is asking to cover all skills of each…
We consider the problem of simultaneous approximation to a number and to its square in a general framework that encompasses imaginary quadratic number fields and fields of rational functions in one variable. In this context, we construct…
We study the succinctness of the complement and intersection of regular expressions. In particular, we show that when constructing a regular expression defining the complement of a given regular expression, a double exponential size…
This paper focuses on greedy expansions, one possible representation of numbers, and on arithmetical operations with them. Performing addition or multiplication some additional digits can appear. We study bounds on the number of such digits…
Program synthesis is the task of automatically deriving a program that has been specified by a user in advance. Combining automated theorem proving with program synthesis enables the automated construction of proven-to-be-correct programs,…
The Operator axioms have produced new real numbers with new operators. New operators naturally produce new equations and thus extend the traditional mathematical models which are selected to describe various scientific rules. So new…
We formalize and analyze a new problem in formal language theory termed control improvisation. Given a specification language, the problem is to produce an improviser, a probabilistic algorithm that randomly generates words in the language,…