Computer Science

Given an input string s and a specific Lindenmayer system (the so-called Fibonacci grammar), we define an automaton which is capable of (i) determining whether s belongs to the set of strings that the Fibonacci grammar can generate (in other words, if s corresponds to a generation of the grammar) and, if so, (ii) reconstructing the previous generation.

A new method of analyzing rule continuity in computations with shape grammars is presented. By building on recent results in topology for shapes in algebras U i , the paper provides, (1) a general formulation of continuous rule applications based on the continuity of the mappings that describe these rule applications, (2) conditions that a mapping must satisfy to be suitable for analyzing rule continuity, and (3) procedures for computing continuous topologies in a given computation.

In this paper we present a detailed proof of an important result of algebraic logic: namely that the free commutative Kleene algebra is the space of semilinear sets. The first proof of this result was proposed by Redko in 1964, and simplified and corrected by Pilling in his 1970 thesis. However, we feel that a new account of this proof is needed now. This result has acquired a particular importance in recent years, since it is a key component in the completeness proofs of several algebraic models of concurrent computations (bi-Kleene algebra, concurrent Kleene algebra...). To that effect, we present a new proof of this result.

An F-system is a computational model that performs a folding operation on strings of a given language, following directions coded on strings of another given language. This note considers the case in which both given languages are regular, and it shows that such F-system generates linear context-free languages. The demonstration is based on constructing a one-turn pushdown automaton for the generated language.

Automated market makers (AMMs) are one of the most prominent decentralized finance (DeFi) applications. They allow users to exchange units of different types of crypto-assets, without the need to find a counter-party. There are several implementations and models for AMMs, featuring a variety of sophisticated economic mechanisms. We present a theory of AMMs. The core of our theory is an abstract operational model of the interactions between users and AMMs, which can be instantiated with any desired economic design mechanism. We exploit our theory to formally prove a set of fundamental properties of AMMs, characterizing both structural and economic aspects. We do this by abstracting from the actual economic mechanisms used in implementations, by identifying sufficient conditions which ensure the relevant properties. Notably, we devise a general solution to the arbitrage problem, the main game-theoretic foundation behind the economic mechanisms of AMMs.

In this paper we introduce a weighted LTL over product ω -valuation monoids that satisfy specific properties. We also introduce weighted generalized Büchi automata with ε -transitions, as well as weighted Büchi automata with ε -transitions over product ω -valuation monoids and prove that these two models are expressively equivalent and also equivalent to weighted Büchi automata already introduced in the literature. We prove that every formula of a syntactic fragment of our logic can be effectively translated to a weighted generalized Büchi automaton with ε -transitions. We prove that the number of states of the produced automaton is polynomial in the size of the corresponding formula. For restricted product ω -valuation monoids we define a weighted LTL, weighted generalized Büchi automata with ε -transitions, and weighted Büchi automata with ε -transitions, and we prove the aforementioned results for restricted product ω -valuation monoids as well. The translation of weighted LTL formulas to weighted generalized Büchi automata with ε -transitions is now obtained for a restricted syntactical fragment of the logic.

In this document, we propose a description, via a Haskell implementation, of a generalization of the notion of regular expression allowing us to group the definitions and the methods of (tree or word) automata constructions over one generic structure, based on enriched category theory tools. We first recall several methods of conversion from expressions to automata, enlightening the similarities between the words and trees cases. We then produce an original study of the power of enriched category theory applied 1) to automata and expressions implementation, and 2) to the study of associated algorithms, using advanced concepts of functional programming, while simultaneously constructing a Haskell implementation of notions of enriched category theory and associated automata. More precisely, the Haskell implementation and the algebraic definition of the generic automaton structure are based on the following ideas: - enriched categories, enriched functors, enriched monads, etc. can be implemented in Haskell; - Type level programming can be used to properly encode function arity; - monoids (word structure) and operads (tree structure) can be encoded as monoid objects; - tree and word automata can be represented by the same algebraic structure, via enriched categories. This generalization leads to surprising remarks. As an example, some classical algorithms (determinization, completion, conversion from alternating to deterministic automaton) can be regrouped in only one function. We will then define a notion of generalized expressions based on the notion of monoidal tensor product. Haskell sources are available at: this http URL

In this paper, we focus on the design and verification of timed automata (TA). We introduce a new method for assisting construction and verification of TA models along with a tool implementing the proposed method, i.e., ATAC: Automated Timed Automata Construction. Our method provides two main functionalities, i.e., construction of TA models from descriptions and generation of temporal logic queries from specifications. Both description and specification sentences shall follow our well-defined structured natural language definition. TA models constructed from descriptions and temporal logic queries generated from specifications can be imported to UPPAAL, a verification tool for TA models. The goal is to accelerate the design phase for real-time systems by assisting the construction and verification of a formal model. We believe ATAC can be useful especially during the initial phases of the design process and help designers to avoid erroneous models.

We present a general method for computing the abelian complexity ρ ab s (n) of an automatic sequence s in the case where (a) ρ ab s (n) is bounded by a constant and (b) the Parikh vectors of the length- n prefixes of s form a synchronized sequence. We illustrate the idea in detail, using the free software Walnut to compute the abelian complexity of the Tribonacci word TR=0102010⋯ , the fixed point of the morphism 0→01 , 1→02 , 2→0 . Previously, Richomme, Saari, and Zamboni showed that the abelian complexity of this word lies in {3,4,5,6,7} , and Turek gave a Tribonacci automaton computing it. We are able to "automatically" rederive these results, and more, using the method presented here.

We study the abelian period sets of Sturmian words, which are codings of irrational rotations on a one-dimensional torus. The main result states that the minimum abelian period of a factor of a Sturmian word of angle α with continued fraction expansion [0; a 1 , a 2 ,…] is either t q k with 1≤t≤ a k+1 (a multiple of a denominator q k of a convergent of α ) or q k,ℓ (a denominator q k,ℓ of a semiconvergent of α ). This result generalizes a result of Fici et. al stating that the abelian period set of the Fibonacci word is the set of Fibonacci numbers. A characterization of the Fibonacci word in terms of its abelian period set is obtained as a corollary.