Fuzzy automata as coalgebras

The coalgebraic method is of great significance to research in process algebra, modal logic, object-oriented design and component-based software engineering. In recent years, fuzzy control has been widely used in many fields, such as handwriting recognition and the control of robots or air conditioners. It is then an interesting topic to analyze the behavior of fuzzy automata from a coalgebraic point of view. This paper models different types of fuzzy automata as coalgebras with a monad structure capturing fuzzy behavior. Based on the coalgebraic models, we can define a notion of fuzzy language and consider several versions of bisimulation for fuzzy automata. A group of combinators is defined to compose fuzzy automata of two branches: state transition and output function. A case study illustrates the coalgebraic models proposed and their composition.This work has been supported by the Guangdong Science and Technology Department (Grant No. 2018B010107004) and the National Natural Science Foundation of China under grant No. 61772038, 61532019 and 61272160. L.S.B. was supported by the ERDF—European Regional Development Fund through the Operational Programme for Competitiveness and InternationalisationCOMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT, within project KLEE - POCI-01-0145-FEDER-030947

Mathematics in Software Reliability and Quality Assurance

This monograph concerns the mathematical aspects of software reliability and quality assurance and consists of 11 technical papers in this emerging area. Included are the latest research results related to formal methods and design, automatic software testing, software verification and validation, coalgebra theory, automata theory, hybrid system and software reliability modeling and assessment

Derivational Complexity and Context-Sensitive Rewriting

[EN] Context-sensitive rewriting is a restriction of rewriting where reduction steps are allowed on specific arguments mu(f) subset of {1, ..., k} of k-ary function symbols f only. Terms which cannot be further rewritten in this way are called mu-normal forms. For left-linear term rewriting systems (TRSs), the so-called normalization via mu-normalization procedure provides a systematic way to obtain normal forms by the stepwise computation and combination of intermediate mu-normal forms. In this paper, we show how to obtain bounds on the derivational complexity of computations using this procedure by using bounds on the derivational complexity of context-sensitive rewriting. Two main applications are envisaged: Normalization via mu-normalization can be used with non-terminating TRSs where the procedure still terminates; on the other hand, it can be used to improve on bounds of derivational complexity of terminating TRSs as it discards many rewritings.Partially supported by the EU (FEDER), and projects RTI2018-094403-B-C32 and PROMETEO/2019/098.Lucas Alba, S. (2021). Derivational Complexity and Context-Sensitive Rewriting. Journal of Automated Reasoning. 65(8):1191-1229. https://doi.org/10.1007/s10817-021-09603-11191122965

Semantic web and formal design methods

Ph.DDOCTOR OF PHILOSOPH

A formal modeling approach to ontology engineering

Ph.DDOCTOR OF PHILOSOPH