6,564 research outputs found
Ground Confluence Prover based on Rewriting Induction
Ground confluence of term rewriting systems guarantees that all ground
terms are confluent. Recently, interests in proving confluence of
term rewriting systems automatically has grown, and confluence provers
have been developed. But they mainly focus on confluence and not
ground confluence. In fact, little interest has been paid to
developing tools for proving ground confluence automatically. We
report an implementation of a ground confluence prover based on
rewriting induction, which is a method originally developed for
proving inductive theorems
Improving Rewriting Induction Approach for Proving Ground Confluence
In (Aoto&Toyama, FSCD 2016), a method to prove ground confluence of many-sorted term rewriting systems based on rewriting induction is given. In this paper, we give several methods that add wider flexibility to the rewriting induction approach for proving ground confluence. Firstly, we give a method to deal with the case in which suitable rules are not presented in the input system. Our idea is to construct additional rewrite rules that supplement or replace existing rules in order to obtain a set of rules that is adequate for applying rewriting induction. Secondly, we give a method to deal with non-orientable constructor rules. This is accomplished by extending the inference system of rewriting induction and giving a sufficient criterion for the correctness of the system. Thirdly, we give a method to deal with disproving ground confluence. The presented methods are implemented in our ground confluence prover AGCP and experiments are reported. Our experiments reveal the presented methods are effective to deal with problems for which state-of-the-art ground confluence provers can not handle
A general conservative extension theorem in process algebras with inequalities
We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity, that is, provable transitions from an original term in the extension are the same as in the original system. As a simple corollary of the conservative extension theorem we prove a completeness theorem. We also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one. We provide many applications to show that our results are useful. The applications include (but are not limited to) various real and discrete time settings in ACP, ATP, and CCS and the notions projection, renaming, stage operator, priority, recursion, the silent step, autonomous actions, the empty process, divergence, etc
Deciding Confluence and Normal Form Properties of Ground Term Rewrite Systems Efficiently
It is known that the first-order theory of rewriting is decidable for ground
term rewrite systems, but the general technique uses tree automata and often
takes exponential time. For many properties, including confluence (CR),
uniqueness of normal forms with respect to reductions (UNR) and with respect to
conversions (UNC), polynomial time decision procedures are known for ground
term rewrite systems. However, this is not the case for the normal form
property (NFP). In this work, we present a cubic time algorithm for NFP, an
almost cubic time algorithm for UNR, and an almost linear time algorithm for
UNC, improving previous bounds. We also present a cubic time algorithm for CR
Observation of implicit complexity by non confluence
We propose to consider non confluence with respect to implicit complexity. We
come back to some well known classes of first-order functional program, for
which we have a characterization of their intentional properties, namely the
class of cons-free programs, the class of programs with an interpretation, and
the class of programs with a quasi-interpretation together with a termination
proof by the product path ordering. They all correspond to PTIME. We prove that
adding non confluence to the rules leads to respectively PTIME, NPTIME and
PSPACE. Our thesis is that the separation of the classes is actually a witness
of the intentional properties of the initial classes of programs
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