3 research outputs found
Policy Iteration-based Conditional Termination and Ranking Functions
The final publication is available at link.springer.com.International audienceTermination analyzers generally synthesize ranking functions or relations, which represent checkable proofs of their results. In [], we proposed an approach for conditional termination analysis based on abstract fixpoint computation by policy iteration. This method is not based on ranking functions and does not directly provide a ranking relation, which makes the comparison with existing approaches difficult. In this paper we study the relationships between our approach and ranking functions and relations, focusing on extensions of linear ranking functions. We show that it can work on programs admitting a specific kind of segmented ranking functions, and that the results can be checked by the construction of a disjunctive ranking relation. Experimental results show the interest of this approach
On the Decidability of Termination for Polynomial Loops
We consider the termination problem for triangular weakly non-linear loops (twn-loops) over some ring like , , or . Essentially, the guard of such a loop is an arbitrary Boolean formula over (possibly non-linear) polynomial inequations, and the body is a single assignment where each is a variable, , and each is a (possibly non-linear) polynomial over and the variables . We present a reduction from the question of termination to the existential fragment of the first-order theory of and . For loops over , our reduction entails decidability of termination. For loops over and , it proves semi-decidability of non-termination. Furthermore, we present a transformation to convert certain non-twn-loops into twn-form. Then the original loop terminates iff the transformed loop terminates over a specific subset of , which can also be checked via our reduction. This transformation also allows us to prove tight complexity bounds for the termination problem for two important classes of loops which can always be transformed into twn-loops