Outlook

Abstract

AbstractWe considered the connection between logic and games underlying model-checking procedures on finite structures and extended it to the class of automatic structures. To this end we defined a new class of hierarchical games suitable for model-checking first-order logic over automatic structures. These games can be used not only for first-order logic, but also for formulas with the regular game quantifier. Moreover, cardinality and counting quantifiers can be reduced to first-order logic on automatic structures. Thus, hierarchical games provide a way to model-check first-order logic extended with cardinality, counting and game quantification on automatic presentations.