The Expressiveness of Looping Terms in the Semantic Programming
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We consider the complexity of reasoning in extensions of the language of Δ_0-formulas with non-standard list terms, which represent bounded list search, bounded recursion, and bounded iteration. We provide a number of complexity bounds on model checking and satisfiability for these formulas. In particular, we show that the set of Δ_0-formulas with bounded recursive terms true in a given list superstructure HW(M) is non-elementary (i.e., it contains the class kEXPTIME, for all k≥ 1). For Δ_0-formulas with bounded iteration or restricted usage of recursive terms, we show lower complexity.
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