Input Test

Given an input string, this function shows step-by-step the states that the automaton goes through when it is run on the input.

Input Format

1. Words of propositional symbols



We assume propositional symbols are like {p, ~p}, {p q, p ~q, ~p q, ~p ~q}, etc. Each symbol in the input word should be enclosed in a pair of parentheses "(" and ")". The infinite repetition of the last portion of the input is indicated by enclosing the portion in a pair of curry braces "{" and "}".


Examples:
• Intended input: ppp~pp~pp // which is a finite string
  Real format: (p)(p)(p)(~p)(p)(~p)(p)
  Abbreviation (only one proposition and one character): ppp~pp~pp
• Intended input: ppp~pp(~pp)^ω // where ω means an infinite repetition
  Real format: (p)(p)(p)(~p)(p){(~p)(p)}
  Abbreviation (only one proposition and one character): ppp~pp{~pp}
• Intended input: (~pq)((~pq)(~p~q)(~p~q))^ω
  Real format: (~p q){(~p q)(~p ~q)(~p ~q)} // blank space between propositions



2. Words of classical symbols



We assume the alphabet is like {go, stop, turn}, {red, green, blue}, {r, g, b}, etc. Each symbol in the input word should be enclosed in a pair of parentheses "(" and ")". The infinite repetition of the last portion of the input is indicated by enclosing the portion in a pair of curry braces "{" and "}".


Examples:
• Intended input: rgbbgrg // which is a finite string
  Real format: (r)(g)(b)(b)(g)(r)(g)
  Abbreviation (single character only): rgbbgrg
• Intended input: rgbbg(rg)^ω // where ω means an infinite repetition
  Real format: (r)(g)(b)(b)(g){(r)(g)}
  Abbreviation (single character only): rgbbg{rg}
• Intended input: (go)((turn)(stop)(go))^ω
  Real format: (go){(stop)(turn)(go)}