The Size of Power Automata

We describe a class of simple transitive semiautomata that exhibit full exponential blow-up during deterministic simulation. For arbitrary semiautomata we show that it is PSPACE-complete to decide whether the size of the accessible part of their power automata exceeds a given bound. 1 Motivation Consider the following semiautomaton A = [n], Σ, δ where [n] = {1, . . . , n}, Σ = {a, b, c} and the transition function is given by δa a cyclic shift on [n], δb the transposition that interchanges 1 and 2, δc sends 1 and 2 to 2, identity elsewhere. It is well-known that A has a transition semigroup of maximal size nn, see [13]. In other words, every function f : [n] → [n] is already of the form δw for some word w. Note that δa, δb can be replaced by any other pair of generators for the symmetric group on n points, and δc can be replaced by any function whose range

• Type: Conference
• Year: 2001
• Where: MFCS
• Authors: Klaus Sutner
• Keywords: Exponential Blow-up, Maximal Size Nn, MFCS 2001, Simple Transitive Semiautomata, Theoretical Computer Science