Abstract
Total program correctness includes partial program correctness and program termination. These two subproblems are undecidable for general programs. As the predominant part of total correctness, the partial program correctness was studied intensively by the research community. Nevertheless, proving termination for an arbitrary program is challenging. This paper describes an automated method that tests for termination of modulo-case functions by conducting a mathematical induction proof. The system takes a modulo-case function and builds an execution trace tree from its inverse. Then, a linear polynomial is formed to capture the level of the executed trace tree for which the termination problem holds. Using the cases of the original function, an inductive proof is automatically generated. If a function successfully terminates, its runtime is computed based on the polynomial.
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Andrei, S., Doss, K., Makki, S.K. (2012). Proof Automation of Program Termination. In: Qian, Z., Cao, L., Su, W., Wang, T., Yang, H. (eds) Recent Advances in Computer Science and Information Engineering. Lecture Notes in Electrical Engineering, vol 125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25789-6_61
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DOI: https://doi.org/10.1007/978-3-642-25789-6_61
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