Leftmove-bounded picture languages

• Published in: Theoretical computer science Vol. 237; no. 1; pp. 183 - 195
• Main Authors: Kim, Changwook, Sudborough, Ivan Hal
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 28.04.2000; Elsevier
• Subjects: Applied sciences; Chain code; Complexity; Computer science; control theory; systems; Exact sciences and technology; Formal languages; Language theory and syntactical analysis; Picture languages; Theoretical computing; Chain code; Picture languages; Formal languages; Complexity; Formal language; Picture language
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/S0304-3975(98)00164-9

Let Π = {u,d,r,l} be the chain-code picture alphabet such that u (d,r,l) denotes the graphics command to move the drawing pen up (down, right, left) in the 2D Cartesian plane. It is known that the picture membership problem can be solved in polynomial time for each context-free language over {u,d,r} and is NP-complete for a so-called retreat-bounded regular (or reversal-bounded linear) language over Π. Imposing both retreat and reversal bounds on languages over Π results in the leftmove-bounded languages whose words describe pictures by making no more than a bounded number of left moves. The picture membership problem can be solved in polynomial time for each leftmove-bounded context-free language over Π and is NP-complete for a leftmove-unbounded (but retreat-bounded) linear language over {u,d,lr}. There exists a context-sensitive language over {u,d,r} (or {u,d,lr}) for which the picture membership problem is undecidable.