We show the surprising result that the cutpoint isolation problem is decidable for probabilistic finite automata where input words are taken from a letter-monotonic context-free language. A context-free language L is letter-monotonic when L \subseteq a_1^*a_2^* \cdots a_\ell^* for some finite \ell > 0 where each letter is distinct. A cutpoint is isolated when it cannot be approached arbitrarily closely. The decidability of this problem is in marked contrast to the situation for the (strict) emptiness problem for PFA which is undecidable under the even more severe restrictions of PFA with polynomial ambiguity, commutative matrices and input over a letter-monotonic language as well as  the injectivity problem which is undecidable for PFA over letter-monotonic languages. We provide a constructive nondeterministic algorithm to solve the cutpoint isolation problem, even for exponentially ambiguousPFA, and we also show that the problem is at least NP-hard  .
We show the surprising result that the cutpoint isolation problem is decidable for Probabilistic Finite Automata (PFA) where input words are taken from a letter-bounded context-free language. A context-free language \mathcal{L \subseteq a_1^*a_2^* \cdots a_\ell^* for some finite \ell > 0 where each letter is distinct. A cutpoint is isolated when it cannot be approached arbitrarily closely. The decidability of this problem is in marked contrast to the situation for the (strict) emptiness problem for PFA which is undecidable under the even more severe restrictions of PFA with polynomial ambiguity, commutative matrices and input over a letter-bounded language as well as to the injectivity problem which is undecidable for PFA over letter-bounded languages. We provide a constructive nondeterministic algorithm to solve the cutpoint isolation problem, which holds even when the PFA is exponentially ambiguous. We also show that the problem is at least NP-hard and use our decision procedure to solve several related problems .
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probabilistic finite automata
Probabilistic Finite Automata (PFA)
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letter-monotonic
letter-bounded
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L is letter-monotonic when L
\mathcal{L
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letter-monotonic
letter-bounded
A
to
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letter-monotonic
letter-bounded
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even for exponentially ambiguousPFA, and we
which holds even when the PFA is exponentially ambiguous. We
A
and use our decision procedure to solve several related problems