On reversal-bounded picture languages

Abstract

For an integer k⩾0, a k-reversal-bounded picture language is a chain-code picture language which is described by a language L over the alphabet π = { u, d, r, l} such that, for every word x in L, the number of alternating occurrences of r's and l's in x is bounded by k. It is shown that the membership problem can be solved in O( n 4 k + 4 ) time for k-reversal-bounded regular picture languages, for every k⩾1, and is NP-complete for 1-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 12) time) for 0-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.