Related papers: Automatic Theorem-Proving in Combinatorics on Word…
We introduce a new class of automata (which we coin EU-automata) running on infininte trees of arbitrary (finite) arity. We develop and study several algorithms to perform classical operations (union, intersection, complement, projection,…
In this paper we describe an approach to constraint-based syntactic theories in terms of finite tree automata. The solutions to constraints expressed in weak monadic second order (MSO) logic are represented by tree automata recognizing the…
Methods for specifying Moore type state machines (transducers) abstractly via primitive recursive functions and for defining parallel composition via simultaneous primitive recursion are discussed. The method is mostly of interest as a…
Symbolic automata are finite state automata that support potentially infinite alphabets, such as the set of rational numbers, generally applied to regular expressions/languages over finite words. In symbolic automata (or automata modulo…
We contribute results for a set of fundamental problems in the context of programmable matter by presenting algorithmic methods for evaluating and manipulating a collective of particles by a finite automaton that can neither store…
We study the computational power of real-time finite automata that have been augmented with a vector of dimension k, and programmed to multiply this vector at each step by an appropriately selected $k \times k$ matrix. Only one entry of the…
We study a well-known technique of using absoluteness for giving choice-free proofs to some statements which are known to be provable with the axiom of choice. The idea is to reduce the problem to an inner model where the axiom of choice…
We study subsystems of open induction which are strongly connected to methods of automated inductive theorem proving. Specifically, we consider systems obtained from restricting induction to atoms, literals, clauses, and dual clauses. We…
There is a fundamental difficulty in generalizing weighted automata to the case of infinite words: in general the infinite sum-of-products from which the weight of a given word is derived will diverge. Many solutions to this problem have…
We present a polynomial-time algorithm that determines, given some choice rule, whether there exists an obviously strategy-proof mechanism for that choice rule.
The paper explores combinatorial properties of Fibonacci words and their generalizations within the framework of combinatorics on words. These infinite sequences, measures the diversity of subwords in Fibonacci words, showing non-decreasing…
The representation theory of the symmetric groups S_n is intimately related to combinatorics: combinatorial objects such as Young tableaux and combinatorial algorithms such as Murnaghan-Nakayama rule. In the limit as n tends to infinity,…
We present a novel automata-based approach to address linear temporal logic modulo theory (LTL-MT) as a specification language for data words. LTL-MT extends LTL_f by replacing atomic propositions with quantifier-free multi-sorted…
Although reasoning about equations over strings has been extensively studied for several decades, little research has been done for equational reasoning on general clauses over strings. This paper introduces a new superposition calculus…
We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in…
Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…
Recently, in weighted automata theory the weight structure of strong bimonoids has found much interest; they form a generalization of semirings and are closely related to near-semirings studied in algebra. Here, we define polynomials over a…
Let $t(n)$ denote the number of $1$-bits in the base-$2$ representation of $n$, taken modulo $2$. We show how to prove the classic conjecture of Leo Moser, on the rarefied sum $\sum_{0\leq i<n} (-1)^{t(3i)}$, using tools from automata…
The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…
The theory of abstract argumentation frameworks (afs) has, in the main, focused on finite structures, though there are many significant contexts where argumentation can be regarded as a process involving infinite objects. To address this…