Transforming structures by set interpretations

We consider a new kind of interpretation over relational structures: finite sets interpretations. Those interpretations are defined by weak monadic second-order (WMSO) formulas with free set variables. They transform a given structure into a structure with a domain consisting of finite sets of elements of the orignal structure. The definition of these interpretations directly implies that they send structures with a decidable WMSO theory to structures with a decidable first-order theory. In this paper, we investigate the expressive power of such interpretations applied to infinite deterministic trees. The results can be used in the study of automatic and tree-automatic structures.Comment: 36 page

On the Languages Accepted by Watson-Crick Finite Automata with Delays

[EN] In this work, we analyze the computational power of Watson-Crick finite automata (WKFA) if some restrictions over the transition function in the model are imposed. We consider that the restrictions imposed refer to the maximum length difference between the two input strands which is called the delay. We prove that the language class accepted by WKFA with such restrictions is a proper subclass of the languages accepted by arbitrary WKFA in general. In addition, we initiate the study of the language classes characterized by WKFAs with bounded delays. We prove some of the results by means of various relationships between WKFA and sticker systems.This work has been developed with the financial support of the European Union's Horizon 2020 research and innovation programme under grant agreement No. 952215 corresponding to the TAILOR project.Sempere Luna, JM. (2021). On the Languages Accepted by Watson-Crick Finite Automata with Delays. Mathematics. 9(8):1-12. https://doi.org/10.3390/math9080813S1129

Weighted Automata Computation of Edit Distances with Consolidations and Fragmentations

International audienceWe study edit distances between strings, based on operations of character substitutions, insertions, deletions and additionally consolidations and fragmentations. The two latter operations transform a sequence of characters into one character and vice-versa. They correspond to the compression and expansion in Dynamic Time-Warping algorithms for speech recognition and are also used for the formal analysis of written music.Such edit distances are not computable in general for arbitrary rulesets. We propose weighted automaton constructions to compute an edit distance taking into account both consolidations and deletions, or both fragmentations and insertions. Assuming that the operation ruleset has a constant size, these constructions are polynomial into the lengths of the involved strings. We finally show that the optimal weight of sequences made of consolidations chained with fragmentations, in that order, is computable for arbitrary rulesets, and not computable if we reverse the order of fragmentations and consolidations

Unification and Logarithmic Space

We present an algebraic characterization of the complexity classes Logspace and Nlogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is rooted in proof theory and more specifically linear logic and geometry of interaction. We show how to build a model of computation in the unification algebra and then, by means of a syntactic representation of finite permutations in the algebra, we prove that whether an observation (the algebraic counterpart of a program) accepts a word can be decided within logarithmic space. Finally, we show that the construction naturally corresponds to pointer machines, a convenient way of understanding logarithmic space computation.Comment: arXiv admin note: text overlap with arXiv:1402.432

An ontology for specifying and tracing requirements engineering artifacts and Test Artifacts

Nowadays, modern software development processes follow an iterative approach, which makes possible to start the testing of a system at early stages. This approach requires recording the requirements artifacts that specify the functionality or characteristics required by the system, and the test cases that are derived from each requirement artifact. Frequently, software development organizations employ supporting tools to create and maintain these artifacts. There exist numerous tools for supporting requirements specification activities, as well as the definition and execution of test cases. These separate tools have their own databases and metamodels. The lack of integration between these tools leads to difficulties in tracing related artifacts and obtaining useful knowledge to manage the developing process. It is necessary to understand without ambiguities the concepts used by the different tools to allow them to interoperate. This paper proposes an ontology that defines and integrates the concepts included by the metamodels of different Requirements Engineering and Testing Management supporting tools. The formalization of these concepts and their relationships in an ontology language prevents ambiguity of the concepts and permit to the tools involved to interoperate with each other, to achieve semantic consistency and the tracing of artifacts. The proposed ontology used in conjunction with a reasoner provides capabilities to infer traces that are not explicit, which makes it possible to easily maintain artifacts and associations between them. The approach facilitates backward tracing from test cases to use cases and functional requirements artifacts, obtain knowledge about the causes of a defect or a poor specification, and enable impact analysis.Fil: Roldán, María Luciana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo y Diseño. Universidad Tecnológica Nacional. Facultad Regional Santa Fe. Instituto de Desarrollo y Diseño; ArgentinaFil: Vegetti, Maria Marcela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo y Diseño. Universidad Tecnológica Nacional. Facultad Regional Santa Fe. Instituto de Desarrollo y Diseño; ArgentinaFil: Gonnet, Silvio Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo y Diseño. Universidad Tecnológica Nacional. Facultad Regional Santa Fe. Instituto de Desarrollo y Diseño; ArgentinaFil: Marciszack, Marcelo Martín. Universidad Tecnológica Nacional. Facultad Regional Córdoba; ArgentinaFil: Leone, Horacio Pascual. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo y Diseño. Universidad Tecnológica Nacional. Facultad Regional Santa Fe. Instituto de Desarrollo y Diseño; Argentin