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There has been a growing interest in defining models of automata enriched with time, such as finite automata extended with clocks (timed automata). In this paper, we study deterministic timed finite state machines (TFSMs), i.e., finite…
We contribute to the refined understanding of the language-logic-algebra interplay in the context of first-order properties of countable words. We establish decidable algebraic characterizations of one variable fragment of FO as well as…
The connection between languages defined by computational models and logic for languages is well-studied. Monadic second-order logic and finite automata are shown to closely correspond to each-other for the languages of strings, trees, and…
In this work a state transformation is presented that transforms a given state-space system to a normal form related to mechanical systems. The underlying state-space system must meet certain requirements such that a transformation exist.…
We study the first-order primal infon logic. It is the core of the policy language DKAL. We provide Gentzen-style calculi for two versions of this logic that are not equivalent. For both versions we investigate the semantics: one of them is…
Large language models (LLMs) have achieved remarkable results on tasks framed as reasoning problems, yet their true ability to perform procedural reasoning, executing multi-step, rule-based computations remains unclear. Unlike algorithmic…
The notion of "closed systems" in Quantum Mechanics is discussed. For this purpose, we study two models of a quantum-mechanical system $P$ spatially far separated from the "rest of the universe" $Q$. Under reasonable assumptions on the…
(abridged) In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of…
The paper considers epistemic properties of linear communication chains. It describes a sound and complete logical system that, in addition to the standard axioms of S5 in a multi-modal language, contains two non-trivial axioms that capture…
Time-space tradeoff has been studied in a variety of models, such as Turing machines, branching programs, and finite automata, etc. While communication complexity as a technique has been applied to study finite automata, it seems it has not…
We study multidimensional cheap talk with simple language and aligned preferences. An expert communicates with a decision-maker using a score that aggregates a multidimensional state into a one-dimensional message. Even though the expert…
We demonstrate the capability of continuous variable Gaussian states to communicate multipartite quantum information. A quantum teamwork protocol is presented according to which an arbitrary possibly entangled multimode state can be…
Stochastic switched systems are a relevant class of stochastic hybrid systems with probabilistic evolution over a continuous domain and control-dependent discrete dynamics over a finite set of modes. In the past few years several different…
The logic of information flows (LIF) is a general framework in which tasks of a procedural nature can be modeled in a declarative, logic-based fashion. The first contribution of this paper is to propose semantic and syntactic definitions of…
Finite-state transducers give efficient representations of many Natural Language phenomena. They allow to account for complex lexicon restrictions encountered, without involving the use of a large set of complex rules difficult to analyze.…
We explore a natural class of semigroups that have word problem decidable by finite state automata. Among the main results are invariance of this property under change of generators, invariance under basic algebraic constructions and…
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…
First-Order Logic (FOL) is widely regarded as one of the most important foundations for knowledge representation. Nevertheless, in this paper, we argue that FOL has several critical issues for this purpose. Instead, we propose an…
By fundamental results of Sch\"utzenberger, McNaughton and Papert from the 1970s, the classes of first-order definable and aperiodic languages coincide. Here, we extend this equivalence to a quantitative setting. For this, weighted automata…
This paper brings cooperative protocols for multi-agent systems with agents having a finite state-space. Both scalar single-integrator consensus and general LTI systems synchronization are considered. Systems having a finite state-space…