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A simple linear-time algorithm for constructing a linear context-free tree grammar of size O ( r g + r g log ⁡ ( n / r g ) ) for a given input tree T of size n is presented, where g is the size of a minimal linear context-free tree grammar for T , and r is the maximal rank of symbols in T (which is a constant in many applications). This is the first example of a grammar-based tree compression algorithm with a good, i.e. logarithmic in terms of the size of the input tree, approximation ratio. The analysis of the algorithm uses an extension of the recompression technique from strings to trees. [ABSTRACT FROM AUTHOR]

It is shown that membership in rational subsets of wreath products H ≀ V with H a finite group and V a virtually free group is decidable. On the other hand, it is shown that there exists a fixed finitely generated submonoid in the wreath product Z ≀ Z with an undecidable membership problem. [ABSTRACT FROM AUTHOR]

Abstract: The computational complexity of the isomorphism problem for regular trees, regular linear orders, and regular words is analyzed. A tree is regular if it is isomorphic to the prefix order on a regular language. In case regular languages are represented by NFAs (DFAs), the isomorphism problem for regular trees turns out to be -complete (resp. -complete). In case the input automata are acyclic NFAs (acyclic DFAs), the corresponding trees are (succinctly represented) finite trees, and the isomorphism problem turns out to be -complete (resp. -complete). A linear order is regular if it is isomorphic to the lexicographic order on a regular language. A polynomial time algorithm for the isomorphism problem for regular linear orders (and even regular words, which generalize the latter) given by DFAs is presented. This solves an open problem by Ésik and Bloom. Similar techniques can be used to show that one can check in polynomial time whether a given regular linear order has a non-trivial automorphism. This improves a recent decidability result of Kuske. [Copyright &y& Elsevier]

Abstract: Tight connections between leaf languages and strings compressed by straight-line programs (SLPs) are established. It is shown that the compressed membership problem for a language L is complete for the leaf language class defined by L via logspace machines. A more difficult variant of the compressed membership problem for L is shown to be complete for the leaf language class defined by L via polynomial time machines. As a corollary, it is shown that there exists a fixed linear visibly pushdown language for which the compressed membership problem is PSPACE-complete. For XML languages, it is shown that the compressed membership problem is coNP-complete.Furthermore it is shown that the embedding problem for SLP-compressed strings is hard for PP (probabilistic polynomial time). [Copyright &y& Elsevier]

Abstract: This paper investigates the word problem for inverse monoids generated by a set Γ subject to relations of the form e = f, where e and f are both idempotents in the free inverse monoid generated by Γ. It is shown that for every fixed monoid of this form the word problem can be solved both in linear time on a RAM as well as in deterministic logarithmic space, which solves an open problem of Margolis and Meakin. For the uniform word problem, where the presentation is part of the input, EXPTIME-completeness is shown. For the Cayley-graphs of these monoids, it is shown that the first-order theory with regular path predicates is decidable. Regular path predicates allow to state that there is a path from a node x to a node y that is labeled with a word from some regular language. As a corollary, the decidability of the generalized word problem is deduced. [Copyright &y& Elsevier]

Abstract: When a process is capable of executing an unbounded number of non-observable actions it is said to be divergent. Different capabilities of an observer to identify this phenomena along the execution leads to different divergent sensitive semantics. This paper develops sound and complete axiomatisations for the divergence sensitive spectrum of weak bisimulation equivalence. The axiomatisations separates the axioms concerning recursion and those that capture the essence of diverging behaviour. [Copyright &y& Elsevier]

Message sequence charts (MSCs) and high-level message sequence charts (HMSCs) are popular formalisms for the specification of communication protocols between asynchronous processes. An important concept in this context is the size of the communication buffers used between processes. Since real systems impose limitations on the capacity (or speed) of communication links, we ask whether a given HMSC can be implemented with respect to a given buffer size imposed by the environment. We introduce four different measures for buffer sizes and investigate for each of these measures the complexity of deciding whether a given MSC (or HMSC, or nested MSC) satisfies a given bound on the buffer size. The complexity of these problems varies between the classes P, NP, and coNP. [Copyright &y& Elsevier]