Related papers: Termination of Rewriting with Right-Flat Rules Mod…
The theory of finite and infinitary term rewriting is extensively developed for orthogonal rewrite systems, but to a lesser degree for weakly orthogonal rewrite systems. In this note we present some contributions to the latter case of weak…
We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating…
First-order applicative term rewriting systems provide a natural framework for modeling higher-order aspects. In earlier work we introduced an uncurrying transformation which is termination preserving and reflecting. In this paper we…
We consider the problem of model--checking for Process Rewrite Systems (PRSs) in normal form. In a PRS in normal form every rewrite rule either only deals with procedure calls and procedure termination, possibly with value return, (this…
Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T. If a sound and complete inference system for…
We consider the model checking problem for Process Rewrite Systems (PRSs), an infinite-state formalism (non Turing-powerful) which subsumes many common models such as Pushdown Processes and Petri Nets. PRSs can be adopted as formal models…
All current investigations to analyze the derivational complexity of term rewrite systems are based on a single termination method, possibly preceded by transformations. However, the exclusive use of direct criteria is problematic due to…
The rewriting system sigma is the set of rules propagating explicit substitutions in the lambda-calculus with explicit substitutions. In this note, we prove the undecidability of unification modulo sigma.
This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic,…
We study Linear Temporal Logic Modulo Theories over Finite Traces (LTLfMT), a recently introduced extension of LTL over finite traces (LTLf) where propositions are replaced by first-order formulas and where first-order variables referring…
We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite…
We revisit completion modulo equational theories for left-linear term rewrite systems where unification modulo the theory is avoided and the normal rewrite relation can be used in order to decide validity questions. To that end, we give a…
Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even…
We over-approximate reachability sets in string rewriting by languages defined by admissible factors, called tiles. A sparse set of tiles contains only those that are reachable in derivations, and is constructed by completing an automaton.…
Logically constrained term rewriting is a relatively new rewriting formalism that naturally supports built-in data structures, such as integers and bit vectors. In the analysis of logically constrained term rewrite systems (LCTRSs),…
We show that left-linear generalized semi-monadic TRSs effectively preserving recognizability of finite tree languages (are EPRF-TRSs). We show that reachability, joinability, and local confluence are decidable for EPRF-TRSs.
Several authors devised type-based termination criteria for ML-like languages allowing non-structural recursive calls. We extend these works to general rewriting and dependent types, hence providing a powerful termination criterion for the…
Rewriting is a framework for reasoning about functional programming. The dependency pair criterion is a well-known mechanism to analyze termination of term rewriting systems. Functional specifications with an operational semantics based on…
Non-confluent and non-terminating constructor-based term rewrite systems are useful for the purpose of specification and programming. In particular, existing functional logic languages use such kind of rewrite systems to define possibly…
In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…