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 ...

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...

Many blame the recent financial market turmoil on malfeasance of ratings agencies, who had incentives to bias their ratings. But these incentives had existed for decades. Why did the ratings bias issue only recently emerge? We model asset issuers who can cherry-pick ratings – observe multiple ratings and disclose only a subset – before auctioning their assets. When assets are simple, agencies’ ...

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...

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...

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.

The need to re-examine established ways of thinking about secularism and its relationship to feminism has arisen in the context of the confluence of a number of developments including: the increasing dominance of the ‘clash of civilizations’ thesis; the expansion of postmodern critiques of Enlightenment rationality to encompass questions of religion; and sustained critiques of the ‘secularizati...

Conditional rewriting has been studied both from the point of view of algebraic data type specifications and as a computational paradigm combining logic and functional programming. An important issue, in either case, is determining whether a rewrite system has the Church-Rosser, or confluence, property. In this paper, we settle negatively the question whether "joinabihty of critical pairs" is, ...