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Observation of String-Rewriting Systems

Cavaliere M., Leupold P.

Fundamenta Informaticae

2006

Vol. 74, nr 4

447-462

Models of computation in theoretical computer science very frequently consist of a device performing some type of process, like a Turing machine and its computation or a grammar and its derivation. After the process halts, only some final output is regarded as the result. In adding an observer to such a device, one can obtain a protocol of the entire process and then use this as the result of the computation. In several recent articles this approach has proved to often exceed greatly the power of the observed system. Here we apply this architecture to string-rewriting systems. They receive a string as input, and a combination of observer and decider then determines whether this string is accepted. This decision is based only on the rewriting process performed. First we determine the power of painter, context-free, and inverse context-free rewriting systems in terms of McNaughton languages. Then these are investigated as components of rewriting/observer systems, and we obtain characterizations of the classes of context-sensitive and recursively enumerable languages. Finally we investigate some limitations, i.e. characterize some systems, where observation does not increase power.

Thue specifications, infinite graphs and synchronized product

Payet E.

Fundamenta Informaticae

2000

Vol. 44, Nr 3

265-290

This paper presents some formal verification-oriented results about the class of graphs associated with Thue specifications. It is shown that this class is closed, up to isomorphism, under synchronized product. It is also established that every rational graph with no edge labeled by the empty word is isomorphic to the graph of a Thue specification. A consequence of this result is that the first-order theory of the graphs of Thue specifications is undecidable. Connections between graphs of Thue specifications and those of Turing machines are finally investigated. The main result is that the graph of each Thue specification is observationally equivalent to that of a Turing machine but the reverse does not hold.

Thue specifications and their monadic second-order properties

Knapik T., Calbrix H.

Fundamenta Informaticae

1999

Vol. 39, Nr 3

305-325

This paper introduces oriented Thue specifications and their models which are simple directed edge-labeled graphs. The monadic second-order theory of these models is investigated and shown decidable for the class of suffix-bounded rational oriented Thue specifications. In addition, a characterization of prefix-closed context-free languages is given in terms of oriented Thue specifications.