Kleene-Schützenberger and Büchi Theorems for Weighted Timed Automata

In 1994, Alur and Dill introduced timed automata as a simple mathematical model for modelling the behaviour of real-time systems. In this thesis, we extend timed automata with weights. More detailed, we equip both the states and transitions of a timed automaton with weights taken from an appropriate mathematical structure. The weight of a transition determines the weight for taking this transition, and the weight of a state determines the weight for letting time elapse in this state. Since the weight for staying in a state depends on time, this model, called weighted timed automata, has many interesting applications, for instance, in operations research and scheduling. We give characterizations for the behaviours of weighted timed automata in terms of rational expressions and logical formulas. These formalisms are useful for the specification of real-time systems with continuous resource consumption. We further investigate the relation between the behaviours of weighted timed automata and timed automata. Finally, we present important decidability results for weighted timed automata

Multi-weighted Automata Models and Quantitative Logics

Recently, multi-priced timed automata have received much attention for real-time systems. These automata extend priced timed automata by featuring several price parameters. This permits to compute objectives like the optimal ratio between rewards and costs. Arising from the model of timed automata, the multi-weighted setting has also attracted much notice for classical nondeterministic automata. The present thesis develops multi-weighted MSO-logics on finite, infinite and timed words which are expressively equivalent to multi-weighted automata, and studies decision problems for them. In addition, a Nivat-like theorem for weighted timed automata is proved; this theorem establishes a connection between quantitative and qualitative behaviors of timed automata. Moreover, a logical characterization of timed pushdown automata is given

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

Logic and Automata

Mathematical logic and automata theory are two scientific disciplines with a fundamentally close relationship. The authors of Logic and Automata take the occasion of the sixtieth birthday of Wolfgang Thomas to present a tour d'horizon of automata theory and logic. The twenty papers in this volume cover many different facets of logic and automata theory, emphasizing the connections to other disciplines such as games, algorithms, and semigroup theory, as well as discussing current challenges in the field