On Reversal-Bounded Picture Languages

Kim, C. and I.H. Sudborough, On reversal-bounded picture languages, Theoretical Computer Science 104 (1992) 185-206. For an integer k >O, a k-reversal-bounded picture language is a chain-code picture language which is described by a language L over the alphabet R= {u,d,r, I} such that, for every word x in L, the number of alternating occurrences of r’s and I’s in x is bounded by k. It is shown that the membership problem can be solved in O(n4’+4 ) time for k-reversal-bounded regular picture languages, for every k> 1, and is NP-complete for l-reversal-bounded stripe linear picture languages. The membership problem is known to be NP-complete for regular and context-free picture languages without restriction on the number of reversals and solvable in O(n) time (O(n’*) time) for O-reversal-bounded regular (context-free) picture languages. Whether the membership problem for stripe context-free picture languages could be solved in polynomial time has been an open problem. Other basic properties of reversal-bounded picture languages are also presented.