Bounded Parikh Automata

Motivation. Adding features to finite automata in order to capture situations beyond regularity has been fruitful to many areas of research. Such features include making the state sets infinite, adding power to the logical characterizations, having the automata operate on infinite domains rather than finite alphabets, adding stack-like mechanisms, etc. (See, e.g., [11, 3, 17, 1].) Model checking and complexity theory below NC2 are areas that have benefited from an approach of this type (e.g., [19, 22]). In such areas, determinism plays a key role and is usually synonymous with a clear understanding of the situation at hand, yet often comes at the expense of other properties, such as expressiveness. Thus, cases where determinism can be achieved without sacrificing other properties are of particular interest.