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The Infimum Problem as a Generalization of the Inclusion Problem for AutomataBorgwardt, Stefan 03 January 2024 (has links)
This thesis is concerned with automata over infinite trees. They are given a labeled infinite tree and accept or reject this tree based on its labels. A generalization of these automata with binary decisions are weighted automata. They do not just decide 'yes' or 'no', but rather compute an arbitrary value from a given algebraic structure, e.g., a semiring or a lattice. When passing from unweighted to weighted formalisms, many problems can be translated accordingly. The purpose of this work is to determine the feasibility of solving the inclusion problem for automata on infinite trees and its generalization to weighted automata, the infimum aggregation problem.
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Weighted Automata with StorageHerrmann, Luisa 01 March 2021 (has links)
In this thesis, we investigate weighted tree automata with storage theoretically. This model generalises finite state automata in three dimensions: (i) from words to trees, (ii) by using an arbitrary storage type in addition to a finite-state control, and (iii) by considering languages in a quantitative setting using a weight structure.
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Multi-weighted Automata Models and Quantitative LogicsPerevoshchikov, Vitaly 06 May 2015 (has links) (PDF)
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.
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Multi-weighted Automata Models and Quantitative LogicsPerevoshchikov, Vitaly 28 April 2015 (has links)
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.
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