TY - JOUR
T1 - When does abstraction help?
AU - Avni, Guy
AU - Kupferman, Orna
PY - 2013
Y1 - 2013
N2 - Abstraction is a leading technique for coping with large state spaces. Abstraction over-approximates the transitions of the original system or the automaton that models it and may introduce nondeterminism. In applications where determinism is essential, we say that an abstraction function is helpful if, after determining and minimizing the abstract automaton, we end up with fewer states than the original automaton. We show that abstraction functions are not always helpful; in fact, they may introduce an exponential blow-up. We study the problem of deciding whether a given abstraction function is helpful for a given deterministic automaton and show that it is PSPACE-complete.
AB - Abstraction is a leading technique for coping with large state spaces. Abstraction over-approximates the transitions of the original system or the automaton that models it and may introduce nondeterminism. In applications where determinism is essential, we say that an abstraction function is helpful if, after determining and minimizing the abstract automaton, we end up with fewer states than the original automaton. We show that abstraction functions are not always helpful; in fact, they may introduce an exponential blow-up. We study the problem of deciding whether a given abstraction function is helpful for a given deterministic automaton and show that it is PSPACE-complete.
KW - Abstraction
KW - Deterministic finite automata
KW - Formal methods
UR - http://www.scopus.com/inward/record.url?scp=84884618379&partnerID=8YFLogxK
U2 - 10.1016/j.ipl.2013.09.007
DO - 10.1016/j.ipl.2013.09.007
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AN - SCOPUS:84884618379
SN - 0020-0190
VL - 113
SP - 901
EP - 905
JO - Information Processing Letters
JF - Information Processing Letters
IS - 22-24
ER -