相关论文: The strength of SCT soundness
We undertake the study of size-change analysis in the context of Reverse Mathematics. In particular, we prove that the SCT criterion is equivalent to $\Sigma^0_2$-induction over RCA$_0$.
Size-Change Termination (SCT) is a method of proving program termination based on the impossibility of infinite descent. To this end we may use a program abstraction in which transitions are described by monotonicity constraints over…
Size-Change Termination (SCT) is a method of proving program termination based on the impossibility of infinite descent. To this end we use a program abstraction in which transitions are described by Monotonicity Constraints over (abstract)…
Termination is an important but undecidable program property, which has led to a large body of work on static methods for conservatively predicting or enforcing termination. One such method is the size-change termination approach of Lee,…
We describe an algorithm for proving termination of programs abstracted to systems of monotonicity constraints in the integer domain. Monotonicity constraints are a non-trivial extension of the well-known size-change termination method.…
Intuitively, if we can prove that a program terminates, we expect some conclusion regarding its complexity. But the passage from termination proofs to complexity bounds is not always clear. In this work we consider Monotonicity Constraint…
In a previous work, the first author extended to higher-order rewriting and dependent types the use of size annotations in types, a termination proof technique called type or size based termination and initially developed for ML-like…
The size-change abstraction (SCA) is an important program abstraction for termination analysis, which has been successfully implemented in many tools for functional and logic programs. In this paper, we demonstrate that SCA is also a highly…
This paper describes an automatic termination checker for a generic first-order call-by-value language in ML style. We use the fact that value are built from variants and tuples to keep some information about how arguments of recursive call…
We present a method for proving that a program running under the Total Store Ordering (TSO) memory model is robust, i.e., all its TSO computations are equivalent to computations under the Sequential Consistency (SC) semantics. This method…
Some type-based approaches to termination use sized types: an ordinal bound for the size of a data structure is stored in its type. A recursive function over a sized type is accepted if it is visible in the type system that recursive calls…
A reliable technique for deductive program verification should be proven sound with respect to the semantics of the programming language. For each different language, the construction of a separate soundness proof is often a laborious…
In mathematical logic there are two seemingly distinct kinds of principles called "reflection principles." Semantic reflection principles assert that if a formula holds in the whole universe, then it holds in a set-sized model. Syntactic…
We present a new approach to proving non-termination of non-deterministic integer programs. Our technique is rather simple but efficient. It relies on a purely syntactic reversal of the program's transition system followed by a…
We investigate the relationship between two independently developed termination techniques. On the one hand, sized-types based termination (SBT) uses types annotated with size expressions and Girard's reducibility candidates, and applies on…
We consider two combinatorial principles, ${\sf{ERT}}$ and ${\sf{ECT}}$. Both are easily proved in ${\sf{RCA}}_0$ plus ${\Sigma^0_2}$ induction. We give two proofs of ${\sf{ERT}}$ in ${\sf{RCA}}_0$, using different methods to eliminate the…
We compare tools for complementing nondeterministic B\"uchi automata with a recent termination-analysis algorithm. Complementation of B\"uchi automata is a key step in program verification. Early constructions using a Ramsey-based argument…
We propose a general proof technique to show that a predicate is sound, that is, prevents stuck computation, with respect to a big-step semantics. This result may look surprising, since in big-step semantics there is no difference between…
We compute and explore numerically the finite system size correction to NLO $2\to2$ scattering in massive scalar $\phi^4$ theory. The derivation uses "denominator regularization" (instead of the usual dimensional regularization) on a…
Conditional term rewriting is an intuitive yet complex extension of term rewriting. In order to benefit from the simpler framework of unconditional rewriting, transformations have been defined to eliminate the conditions of conditional term…