Cost register automata (CRA) are machines reading an input word while computing values using write-only registers: values from registers are combined using the two operations, as well as the constants, of a semiring. Particularly interesting is the subclass of copyless CRAs where the content of a register cannot be used twice for updating the registers. Originally deterministic, non-deterministic variant of CRA may also be defined: the semantics is then obtained by combining the values of all accepting runs with the additive operation of the semiring (as for weighted automata). We show that finitely-ambiguous copyless non-deterministic CRAs (i.e. the ones that admit a bounded number of accepting runs on every input word) can be effectively transformed into an equivalent copyless (deterministic) CRA, without requiring any specific property on the semiring. As a corollary, this also shows that regular look-ahead can effectively be removed from copyless CRAs.
@InProceedings{lopez_et_al:LIPIcs.MFCS.2019.75, author = {Lopez, Th\'{e}odore and Monmege, Benjamin and Talbot, Jean-Marc}, title = {{Determinisation of Finitely-Ambiguous Copyless Cost Register Automata}}, booktitle = {44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)}, pages = {75:1--75:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-117-7}, ISSN = {1868-8969}, year = {2019}, volume = {138}, editor = {Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.75}, URN = {urn:nbn:de:0030-drops-110190}, doi = {10.4230/LIPIcs.MFCS.2019.75}, annote = {Keywords: Cost-register automata, Look-ahead removal, Unambiguity, Determinisation} }
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