Ntyft/ntyxt Rules Reduce to Ntree Rules

Abstract

Groote and Vaandrager introduced the tyft/tyxt format for Transition System Specifications (TSSs), and established that for each TSS in this format that is well-founded, the bisimulation equivalence it induces is a congruence. In this paper, we construct for each TSS in tyft/tyxt format an equivalent TSS that consists of tree rules only. As a corollary we can give an affirmative answer to an open question, namely whether the well-foundedness condition in the congruence theorem for tyft/tyxt can be dropped. These results extend to tyft/tyxt with negative premises and predicates.

Conservative Extension in Positive/Negative Conditional Term Rewriting with Applications to Software Renovation Factories

“…Usually, TSSs need to define a congruence relation with respect to a certain semantics, i.e., if two terms s and t are semantically equivalent, then Con [s] and Con [t] are semantically equivalent for all contexts Con[]. Several formats for TSSs have been developed which guarantee that they define a congruence relation for bisimulation semantics [28,9,3,44,17]. Most CTRSs from the literature do not fit these formats.…”

“…We define a notion of (operational) conservative extension for CTRSs, which is related to an equivalence notion for TSSs in [24,17] …”

Modular Semantics for Transition System Specifications with Negative Premises

“…Earlier results consider open notions of bisimilarity purely positive TSSs (e.g., [7,15,1,18,19]). We hope to use the results here to extend these results to the systems with negative premises (such as those in the (n)tyft/(n)tyxt [13], ntree [9] or PANTH [20] formats).…”

Syntactic Formats for Free: An Abstract Approach to Process Equivalence

“…Firstly, the approach presented here can be extended to deal with other operational preorders and equivalences described in literature. Secondly, one can move from the GSOS format (and its subformats) to the more general (safe) ntree format [9], which can also be formalised in the bialgebraic framework [30]. Thirdly, the abstract framework of test suites seems to be general enough to cover other notions of process behaviour (e.g.…”