A proof-theoretic study of abstract termination principles

We carry out a proof-theoretic analysis of the wellfoundedness of recursive path orders in an abstract setting. We outline a general termination principle and extract from its wellfoundedness proof subrecursive bounds on the size of derivation trees that can be defined in Gödel’s system T plus bar recursion. We then carry out a complexity analysis of these terms and demonstrate how this can be applied to bound the derivational height of term rewrite systems.

Analyzing Runtime Complexity via Innermost Runtime Complexity

There exist powerful techniques to infer upper bounds on the innermost runtime complexity of term rewrite systems (TRSs), i.e., on the lengths of rewrite sequences that follow an innermost evaluation strategy. However, the techniques to analyze the (full) runtime complexity of TRSs are substantially weaker. In this paper, we present a sufficient criterion to ensure that the runtime complexity of a TRS coincides with its innermost runtime complexity. This criterion can easily be checked automatically and it allows us to use all techniques and tools for innermost runtime complexity in order to analyze (full) runtime complexity. By extensive experiments with an implementation of our results in the tool AProVE, we show that this improves the state of the art of automated complexity analysis significantly.

A rewrite-based computational model for functional logic programming

Functional logic programming extends the functional programming style with two important features: the possibility to define nondeterministic operations with overlapping rules, and the usage of logic variables in both defining rules and expressions to evaluate. Conditional constructor-based term rewrite systems (CB-CTRSs) emerged as a suitable model for functional logic programs, because they can be easily transformed into an equivalent program in a core language where computations can be performed more efficiently.We consider a recent proposal by Antoy and Hanus, of translating CB-CTRSs into an equivalent class of programs where computation can be performed by mere rewriting. His computational model has the limitation of computing only ground answer substitutions for equations with strict semantics interpreted as joinability to a value.We propose two adjustments of their computational models, which are capable to compute non-ground answers.

Some Notes on Basic Syntactic Mutation

Unification modulo convergent term rewrite systems is an important research area with many applications. In their seminal paper Lynch and Morawska gave three conditions on rewrite systems that guarantee that unifiability can be checked in polynomial time (P). We show that these conditions are tight, in the sense that relaxing any one of them will "upset the applecart," giving rise to unification problems that are not in P (unless P = NP). We also investigate a related decision problem: we show the undecidability of subterm-collapse for the restricted term rewriting systems that we are considering.

On Implementing Modular Complexity Analysis

We recall the recent approach by (Zankl and Korp, 2010) to prove upper bounds on the (derivational) complexity of term rewrite systems modularly. In this note we show that this approach is suitable to tighten bounds after they have been established. The idea is to replace proof steps with a large bound by (new) proofs that yield smaller bounds. An evaluation of the approach shows the benefits.