We present a complete method for synthesizing lexicographic linear ranking functions (and thus proving termination), supported by inductive invariants, in the case where the transition relation of the program includes disjunctions and existentials (large block encoding of control flow). Previous work would either synthesize a ranking function at every basic block head, not just loop headers, which reduces the scope of programs that may be proved to be terminating, or expand large block transitions including tests into (exponentially many) elementary transitions, prior to computing the ranking function, resulting in a very large global constraint system. In contrast, our algorithm incrementally refines a global linear constraint system according to extremal counterexamples: only constraints that exclude spurious solutions are included. Experiments with our tool Termite show marked performance and scalability improvements compared to other systems.
Regular expressions are part of every programmer’s toolbox. They are used for a wide variety of language-related tasks and there are many algorithms for manipulating them. In particular, matching algorithms that detect whether a word belongs to the language described by a regular expression are well explored, yet new algorithms appear frequently. However, there is no satisfactory methodology for testing such matchers. We propose a testing methodology which is based on generating positive as well as negative examples of words in the language. To this end, we present a new algorithm to generate the language described by a generalized regular expression with intersection and complement operators. The complement operator allows us to generate both positive and negative example words from a given regular expression. We implement our generator in Haskell and OCaml and show that its performance is more than adequate for testing.
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