The rule labeling heuristic aims to establish confluence of (left-)linear term rewrite systems via decreasing diagrams. We present a formalization of a confluence criterion based on the interplay of relative termination and the rule labeling in the theorem prover Isabelle. Moreover, we report on the integration of this result into the certifier CeTA, facilitating the checking of confluence cert...

Confluence that ensures the uniqueness of results of computation is one of important properties on rewriting systems. In this paper, we show undecidability of confluence for length preserving string rewriting systems (SRSs) and prove it by reducing the Post’s correspondence problem (PCP), which is known to be undecidable, to confluence problem of length preserving string rewriting systems. More...

In order to disprove confluence of term rewriting systems, we develop new criteria for ensuring non-joinability of terms based on interpretation and ordering. We present some instances of the criteria which are amenable for automation, and report on an implementation of a confluence disproving procedure based on these instances. The experiments reveal that our method is successfully applied to ...

A strong confluence result for Q, a quantum λ-calculus with measurements, is proved. More precisely, confluence is shown to hold both for finite and infinite computations. The technique used in the confluence proof is syntactical but innovative. This makes Q different from similar quantum lambda calculi, which are either measurement-free or provided with a reduction strategy.

Micro cracks occurring in concrete around tensile rebar is well known latent damage phenomenon. These micro cracks develop, and can be detected after reaching the surface of the concrete. Detection of these cracks before they are fully formed is preferable, but observing the whole crack structure is difficult. Another problem is repairing micro cracks under the concrete surface. The autogenous ...

Confluence is a fundamental property of Constraint Handling Rules (CHR) since, as in other rewriting formalisms, it guarantees that the computations are not dependent on rule application order, and also because it implies the logical consistency of the program declarative view. In this paper we are concerned with proving the confluence of nonterminating CHR programs. For this purpose, we derive...

We study the complexity of the confluence problem for restricted kinds of semi–Thue systems, vector replacement systems and general trace rewriting systems. We prove that confluence for length– reducing semi–Thue systems is P–complete and that this complexity reduces to NC in the monadic case. For length–reducing vector replacement systems we prove that the confluence problem is PSPACE– complet...

The notion of skew confluence was introduced to characterize non-confluent term rewriting systems that had unique infinite normal forms or Böhm like trees. This notion however is not expressive enough to deal with all possible sources of non-confluence in the context of infinite terms or terms extended with letrec. To that end, we present a new notion called ω-skew confluence. We show that ω-sk...

Numerous cracks can be observed in the top coat of thermal barrier coatings (TBCs) deposited by the atmospheric plasma spraying (APS) method. These cracks can be classified into vertical and horizontal ones and they have opposite impact on the properties of TBCs. Vertical cracks reduce the residual stress in the top coat and provide strain tolerance. On the contrary, horizontal cracks trigger d...

In this study, we developed an algorithm for detecting seam cracks in a steel plate. Seam cracks are generated in the edge region of a steel plate. We used the Gabor filter and an adaptive double threshold method to detect them. To reduce the number of pseudo defects, features based on the shape of seam cracks were used. To evaluate the performance of the proposed algorithm, we tested 989 image...