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 -