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Three variables suffice for real-time logic

par Antonopoulos, Timos;Hunter, Paul William ;Raza, Shahab;Worrell, James
Référence Lecture notes in computer science, 9034, page (361-374)
Publication Publié, 2015

Article révisé par les pairs

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Résumé :

A natural framework for real-time specification is monadic first-order logic over the structure (ℝ,<,+1)—the ordered real line with unary +1 function. Our main result is that (ℝ,<,+1) has the 3-variable property: every monadic first-order formula with at most 3 free variables is equivalent over this structure to one that uses 3 variables in total. As a corollary we obtain also the 3-variable property for the structure (ℝ,<, f) for any fixed linear function f : ℝ → ℝ. On the other hand, we exhibit a countable dense linear order (E,<) and a bijection f : E → E such that (E,<, f) does not have the k-variable property for any k.