On the Confluence of Linear Shallow Term Rewrite Systems
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
On the Confluence of Linear Shallow Term Rewrite Systems
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Reachability and confluence are undecidable for flat term rewriting systems
Information Processing Letters
Classes of term rewrite systems with polynomial confluence problems
ACM Transactions on Computational Logic (TOCL)
A new decidability technique for ground term rewriting systems with applications
ACM Transactions on Computational Logic (TOCL)
Confluence of right ground term rewriting systems is decidable
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
The confluence problem for flat TRSs
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
New Undecidability Results for Properties of Term Rewrite Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
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The confluence property of ground (i.e., variable-free) term rewrite systems (GTRS) is well-known to be decidable. This was proved independently in [4, 3] and in [13] using tree automata techniques and ground tree transducer techniques (originated from this problem), yielding EXPTIME decision procedures (PSPACE for strings). Since then, it has been a well-known longstanding open question whether this bound is optimal (see, e.g., [15]).Here we give a polynomial-time algorithm for deciding the confluence of GTRS, and hence as well for the particular case of suffix- and prefix string rewrite systems or Thue systems. We show that this bound is optimal for all these problems by proving PTIME-hardness for the string case. This result may have some impact as well on other areas of formal language theory and, in particular, on the theory of tree automata.