construct a finite automaton (deterministic, nondeterministic, or nondeterministic finite automaton with -transitions) that accepts the language:

(c) The set of all strings over the alphabet a, b, c that yield the same value when evaluated from left to right as right to left by "multiplying" according to the following table in Figure For examples: ((a o b) o b)-(cob)-a and (a o (bo b))-(aoa) a, whereas ((ao b)oc) (coc)b and a b c c ab Figure 1: A non-associative multiplication table for o