Determinancy → (observation EQUIVALENCE = trace equivalence)

AbstractIf an experiment s is conducted on a parallel process p, then, in general, different processes may result from the experiment, due to the nondeterministic behaviour of p (in the notation of Milner (1980): pp′ for different p′. Process p is called determinate if the resulting processes are all equivalent (i.e., if pp′ and pp″, then p′ and p″ are equivalent). This means that, although p behaves nondeterministically, this cannot be detected by an observer of p. Let ⋍ denote observation equivalence, used in CCS (Milner, 1980), let ⋍f denote (the much weaker) failure equivalence, used for CSP (Hoare et al., 1981; Brookes, 1983), and let ⋍t denote (the still weaker) trace equivalence. We show that the three corresponding notions of determinancy are the same, and that for determinate processes ⋍, ⋍f, and ⋍t are the same. Determinacy is preserved under ⋍ and ⋍f, but not under ⋍t

Bottom-up and top-down tree transformations - a comparison

The top-down and bottom-up tree transducer are incomparable with respect to their transformation power. The difference between them is mainly caused by the different order in which they use the facilities of copying and nondeterminism. One can however define certain simple tree transformations, independent of the top-down/bottom-up distinction, such that each tree transformation, top-down or bottom-up, can be decomposed into a number of these simple transformations. This decomposition result is used to give simple proofs of composition results concerning bottom-up tree transformations.\ud \ud A new tree transformation model is introduced which generalizes both the top-down and the bottom-up tree transducer

Three hierarchies of transducers

Composition of top-down tree transducers yields a proper hierarchy of transductions and of output languages. The same is true for ETOL systems (viewed as transducers) and for two-way generalized sequential machines

Hierarchies of hyper-AFLs

For a full semi-AFL K, B(K) is defined as the family of languages generated by all K-extended basic macro grammars, while H(K) B(K) is the smallest full hyper-AFL containing K; a full basic-AFL is a full AFL K such that B(K) = K (hence every full basic-AFL is a full hyper-AFL). For any full semi-AFL K, K is a full basic-AFL if and only if B(K) is substitution closed if and only if H(K) is a full basic-AFL. If K is not a full basic-AFL, then the smallest full basic-AFL containing K is the union of an infinite hierarchy of full hyper-AFLs. If K is a full principal basic-AFL (such as INDEX, the family of indexed languages), then the largest full AFL properly contained in K is a full basic-AFL. There is a full basic-AFL lying properly in between the smallest full basic-AFL and the largest full basic-AFL in INDEX

Top-down tree transducers with regular look-ahead

Top-down tree transducers with regular look-ahead are introduced. It is shown how these can be decomposed and composed, and how this leads to closure properties of surface sets and tree transformation languages. Particular attention is paid to deterministic tree transducers

The copying power of one-state tree transducers

One-state deterministic top-down tree transducers (or, tree homomorphisms) cannot handle "prime copying," i.e., their class of output (string) languages is not closed under the operation L → {$(w$)f(n) w ε L, f(n) ≥ 1}, where f is any integer function whose range contains numbers with arbitrarily large prime factors (such as a polynomial). The exact amount of nonclosure under these copying operations is established for several classes of input (tree) languages. These results are relevant to the extended definable (or, restricted parallel level) languages, to the syntax-directed translation of context-free languages, and to the tree transducer hierarchy.\ud \u