相关论文: Formalized Confluence of Quasi-Decreasing, Strongl…
In this note we give a simple unifying proof of the undecidability of several diagrammatic properties of term rewriting systems that include: local confluence, strong confluence, diamond property, subcommutative property, and the existence…
We present decidability results for termination of classes of term rewriting systems modulo permutative theories. Termination and innermost termination modulo permutative theories are shown to be decidable for term rewrite systems (TRS)…
We present a formalization of basics related to infinite words in the generic proof assistant Isabelle/HOL. Furthermore, we present a formalization of purely morphic and morphic languages. Finally, we present a formalized definition of…
There are many evaluation strategies for term rewrite systems, but proving termination automatically is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies full termination. We adapt…
In a recent paper, new theorems linking apparently unrelated mathematical objects (event structures from concurrency theory and full graphs arising in computational biology) were discovered by cross-site data mining on huge databases, and…
A closure theory is developed for inhomogeneous turbulent flow, which enables a systematic derivation of the turbulence constitutive relations without relying on any empirical parameters. Renormalized-perturbation approximation is performed…
Recently, the well-known dependency pair (DP) framework was adapted to a dependency tuple framework in order to prove almost-sure innermost termination (iAST) of probabilistic term rewrite systems. While this approach was incomplete, in…
We present a formalization of modern SAT solvers and their properties in a form of abstract state transition systems. SAT solving procedures are described as transition relations over states that represent the values of the solver's global…
We report on an inversion tool for a class of oriented conditional constructor term rewriting systems. Four well-behaved rule inverters ranging from trivial to full, partial and semi-inverters are included. Conditional term rewriting…
We give a complete list of formal invariants for a large class of formal differential 1-forms $\w \in \Bbb C [[ x, y]]dx + \Bbb C [[ x, y]]dy$. \indent A $\hat{SL}$-equisingular deformation is an equireducible deformation which leaves…
Convergence of an abstract reduction system (ARS) is the property that any derivation from an initial state will end in the same final state, a.k.a. normal form. We generalize this for probabilistic ARS as almost-sure convergence, meaning…
The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while…
We present a complete formalization in Isabelle/HOL of the object part of an equivalence between L-mosaics and bounded join-semilattices, employing an AI-assisted methodology that integrates large language models as reasoning assistants…
We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…
We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying…
In this thesis, a comprehensive formalization of Milner's Calculus of Communicating Systems (also known as CCS) has been done in HOL theorem prover (HOL4), based on an old work in HOL88. This includes all classical properties of strong/weak…
To analyse cryptographic properties of distributed systems in a systematic way, a formal theory is required. In this paper, we present a theory that allows (1) to specify distributed systems formally, (2) to verify their cryptographic wrt.…
Confluence denotes the property of a state transition system that states can be rewritten in more than one way yielding the same result. Although it is a desirable property, confluence is often too strict in practical applications because…
We propose a functional description of rewriting systems on topological vector spaces. We introduce the topological confluence property as an approximation of the confluence property. Using a representation of linear topological rewriting…
The confluence of untyped \lambda-calculus with unconditional rewriting is now well un- derstood. In this paper, we investigate the confluence of \lambda-calculus with conditional rewriting and provide general results in two directions.…