TY - GEN
T1 - Determinization of Integral Discounted-Sum Automata is Decidable
AU - Almagor, Shaull
AU - Dafni, Neta
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024
Y1 - 2024
N2 - Nondeterministic Discounted-Sum Automata (NDAs) are nondeterministic finite automata equipped with a discounting factor λ>1, and whose transitions are labelled by weights. The value of a run of an NDA is the discounted sum of the edge weights, where the i-th weight is divided by λi. NDAs are a useful tool for modelling systems where the values of future events are less influential than immediate ones. While several problems are undecidable or open for NDA, their deterministic fragment (DDA) admits more tractable algorithms. Therefore, determinization of NDAs (i.e., deciding if an NDA has a functionally-equivalent DDA) is desirable. Previous works establish that when (formula presented), then every complete NDA, namely an NDA whose states are all accepting and its transition function is complete, is determinizable. This, however, no longer holds when the completeness assumption is dropped. We show that the problem of whether an NDA has an equivalent DDA is decidable when λ∈N (in particular, it is in EXPSPACE and is PSPACE-hard).
AB - Nondeterministic Discounted-Sum Automata (NDAs) are nondeterministic finite automata equipped with a discounting factor λ>1, and whose transitions are labelled by weights. The value of a run of an NDA is the discounted sum of the edge weights, where the i-th weight is divided by λi. NDAs are a useful tool for modelling systems where the values of future events are less influential than immediate ones. While several problems are undecidable or open for NDA, their deterministic fragment (DDA) admits more tractable algorithms. Therefore, determinization of NDAs (i.e., deciding if an NDA has a functionally-equivalent DDA) is desirable. Previous works establish that when (formula presented), then every complete NDA, namely an NDA whose states are all accepting and its transition function is complete, is determinizable. This, however, no longer holds when the completeness assumption is dropped. We show that the problem of whether an NDA has an equivalent DDA is decidable when λ∈N (in particular, it is in EXPSPACE and is PSPACE-hard).
KW - Determinization
KW - Discounted Sum Automata
KW - Quantitative Automata
UR - http://www.scopus.com/inward/record.url?scp=85192148401&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-57228-9_10
DO - 10.1007/978-3-031-57228-9_10
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AN - SCOPUS:85192148401
SN - 9783031572272
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 191
EP - 211
BT - Foundations of Software Science and Computation Structures - 27th International Conference, FoSSaCS 2024, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2024, Proceedings
A2 - Kobayashi, Naoki
A2 - Worrell, James
T2 - 27th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2024 held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2024
Y2 - 6 April 2024 through 11 April 2024
ER -