Synthesis and Analysis of Context-Sensitive Languages

Context-sensitive languages are usually omitted in undergraduate textbooks on Theory of Computation or studied only from structural point of view in graduate textbooks with very few classical examples and no techniques of design of context-sensitive grammars and their corresponding linear bounded automata. Here we present a case of study showing that such omission and lack of examples and techniques can be fulfilled using standard techniques of formal languages. In particular it is stablished the descriptional and time complexity of an ambiguous context-sensitive grammar and a deterministic linear bounded automaton for the context-sensitive language L = { a^mb^nc^mn : m, n >= 1}