Formalizing Termination Proofs under Polynomial Quasi-interpretations
نویسنده
چکیده
It is known that (i) programs can be executed in polynomial space if they are compatible with lexicographic path orders (LPOs) and admit polynomial quasi-interpretations (PQIs), and (ii) LPO-termination proofs can be formalized in the Σ2-induction fragment of Peano arithmetic. We show that LPO-termination proofs can be formalized in the second order system U2 of bounded arithmetic if the compatible programs admit PQIs. This together with a well-known characterization of polyspace functions by U2 yields an alternative proof of the fact (i).
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تاریخ انتشار 2015