Equivalence

A $ \mathrm{f}\mathrm{i}_{11\mathrm{a}l}1\mathrm{C}\mathrm{e}$ automaton is a sixtuple $ <\Sigma$ , Q. $ \delta.S,$ $F,$ $f >$ , where $ <\Sigma$ . Q. $ \delta$ . S. $F >$ is a finite automaton, $f$ : $Q \mathrm{x}\Sigma \mathrm{x}Q-R\cup\{-\infty\}$ is a finance function. $R$ is the set of real nulnbers and it holds $f(q,a,q)J=- \infty 1\mathrm{f}\mathrm{f}\sim q’\not\in\delta(q, \mathit{0})$ . The function $f$ is extended to $f$ : $2 ^{Q}\mathrm{x}\Sigma^{*}\mathrm{x}2^{Q}arrow R\cup\{-\infty)\}$ by the plus-max principle. For any $u$ ) $ \in\underline{\nabla}^{\pi}$ . $f(S. \mathrm{t}L. F)$ is the profit of $w$ . It is shown that the equivalence problem of finitely ambiguous finance automata is decidable.