TY - GEN
T1 - On the capacity of capacitated automata
AU - Kupferman, Orna
AU - Sheinvald, Sarai
N1 - Publisher Copyright: © Springer International Publishing Switzerland 2016.
PY - 2016
Y1 - 2016
N2 - Capacitated automata (CAs) have been recently introduced in [8] as a variant of finite-state automata in which each transition is associated with a (possibly infinite) capacity. The capacity bounds the number of times the transition may be traversed in a single run. The study in [8] includes preliminary results about the expressive power of CAs, their succinctness, and the complexity of basic decision problems for them. We continue the investigation of the theoretical properties of CAs and solve problems that have been left open in [8]. In particular, we show that union and intersection of CAs involve an exponential blow-up and that their determinization involves a doubly-exponential blow up. This blow-up is carried over to complementation and to the complexity of the universality and containment problems, which we show to be EXPSPACE-complete. On the positive side, capacities do not increase the complexity when used in the deterministic setting. Also, the containment problem for nondeterministic CAs is PSPACE-complete when capacities are used only in the left-hand side automaton. Our results suggest that while the succinctness of CAs leads to a corresponding increase in the complexity of some of their decision problems, there are also settings in which succinctness comes at no price.
AB - Capacitated automata (CAs) have been recently introduced in [8] as a variant of finite-state automata in which each transition is associated with a (possibly infinite) capacity. The capacity bounds the number of times the transition may be traversed in a single run. The study in [8] includes preliminary results about the expressive power of CAs, their succinctness, and the complexity of basic decision problems for them. We continue the investigation of the theoretical properties of CAs and solve problems that have been left open in [8]. In particular, we show that union and intersection of CAs involve an exponential blow-up and that their determinization involves a doubly-exponential blow up. This blow-up is carried over to complementation and to the complexity of the universality and containment problems, which we show to be EXPSPACE-complete. On the positive side, capacities do not increase the complexity when used in the deterministic setting. Also, the containment problem for nondeterministic CAs is PSPACE-complete when capacities are used only in the left-hand side automaton. Our results suggest that while the succinctness of CAs leads to a corresponding increase in the complexity of some of their decision problems, there are also settings in which succinctness comes at no price.
UR - http://www.scopus.com/inward/record.url?scp=84960369170&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-319-30000-9_24
DO - https://doi.org/10.1007/978-3-319-30000-9_24
M3 - Conference contribution
SN - 9783319299990
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 307
EP - 319
BT - Language and Automata Theory and Applications - 10th International Conference, LATA 2016, Proceedings
A2 - Truthe, Bianca
A2 - Janoušek, Jan
A2 - Dediu, Adrian-Horia
A2 - Martín-Vide, Carlos
PB - Springer Verlag
T2 - 10th International Conference on Language and Automata Theory and Applications, LATA 2016
Y2 - 14 March 2016 through 18 March 2016
ER -