Simple deterministic languages

The s-languages are those languages recognized by a particular restricted form of deterministic pushdown automaton, called an s-machine. They are uniquely characterized by that subset of the standard-form grammars in which each rule has the form Z → aY1...Yn, n≥0, and for which the pairs (Z, a) are distinct among the rules. It is shown that the s-languages have the prefix property, and that they include the regular sets with end-markers. Finally, their closure properties and decision problems are examined, and it is found that their equivalence problem is solvable. Since the solvability of the equivalence problem is not known for arbitrary deterministic languages, the s-languages are the most general class of languages for which this problem has been shown to be solvable.