On Lexicographic Termination Ordering with Space Bound Certifications

We propose a method to analyse the program space complexity, based on termination orderings. This method can be implemented to certify the runspace of programs. We demonstrate that the class of functions computed by first order functional programs over free algebras which terminate by Lexicographic Path Ordering and admit a polynomial quasi-interpretation, is exactly the class of functions computable in polynomial space.

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