14,122 research outputs found
G-automata, counter languages and the Chomsky hierarchy
We consider how the languages of -automata compare with other formal language classes. We prove that if the word problem of a group is accepted by a machine in the class then the language of any -automaton is in the class . It follows that the so called {\emph counter languages} (languages of -automata) are context-sensitive, and further that counter languages are indexed if and only if the word problem for is indexed
Deterministic context-sensitive languages: Part I
A context-sensitive grammar G is said to be CS(k) iff a particular kind of table-driven parser, Tk(G), exists. Corresponding to each Tk(G), we define a class of parsers T¯k(G). Tk(G) is itself a T¯k(G). The main results are:1.Any processor T¯k(G) for a CS(k) grammar G accepts exactly the sentences of G.2.The set of languages generable by CS(k) grammars is exactly the set of languages accepted by deterministic linear-bounded automata (DLBA's).3.(a)It is undecidable whether there exists any k ⩾ 0 such that an arbitrary CSG is CS(k).(b)For every fixed k ⩾ 0, there is no algorithm that will decide if G is CS(k) and also construct Tk(G) if it exists.4.For any DLBA M, algorithms are given to (i) construct a CS(k) grammar GM that generates the language accepted by M, and (ii) construct a processor T¯1(GM).5.CS(k) grammars are unambiguous.6.The sentences of a CS(k) grammar can be parsed in a time proportional to the length of their derivations
On external presentations of infinite graphs
The vertices of a finite state system are usually a subset of the natural
numbers. Most algorithms relative to these systems only use this fact to select
vertices.
For infinite state systems, however, the situation is different: in
particular, for such systems having a finite description, each state of the
system is a configuration of some machine. Then most algorithmic approaches
rely on the structure of these configurations. Such characterisations are said
internal. In order to apply algorithms detecting a structural property (like
identifying connected components) one may have first to transform the system in
order to fit the description needed for the algorithm. The problem of internal
characterisation is that it hides structural properties, and each solution
becomes ad hoc relatively to the form of the configurations.
On the contrary, external characterisations avoid explicit naming of the
vertices. Such characterisation are mostly defined via graph transformations.
In this paper we present two kind of external characterisations:
deterministic graph rewriting, which in turn characterise regular graphs,
deterministic context-free languages, and rational graphs. Inverse substitution
from a generator (like the complete binary tree) provides characterisation for
prefix-recognizable graphs, the Caucal Hierarchy and rational graphs. We
illustrate how these characterisation provide an efficient tool for the
representation of infinite state systems
On Measuring Non-Recursive Trade-Offs
We investigate the phenomenon of non-recursive trade-offs between
descriptional systems in an abstract fashion. We aim at categorizing
non-recursive trade-offs by bounds on their growth rate, and show how to deduce
such bounds in general. We also identify criteria which, in the spirit of
abstract language theory, allow us to deduce non-recursive tradeoffs from
effective closure properties of language families on the one hand, and
differences in the decidability status of basic decision problems on the other.
We develop a qualitative classification of non-recursive trade-offs in order to
obtain a better understanding of this very fundamental behaviour of
descriptional systems
Complete Symmetry in D2L Systems and Cellular Automata
We introduce completely symmetric D2L systems and cellular automata by means of an additional restriction on the corresponding symmetric devices. Then we show that completely symmetric D2L systems and cellular automata are still able to simulate Turing machine computations. As corollaries we obtain new characterizations of the recursively enumerable languages and of some space-bounded complexity classes
Linearly bounded infinite graphs
Linearly bounded Turing machines have been mainly studied as acceptors for
context-sensitive languages. We define a natural class of infinite automata
representing their observable computational behavior, called linearly bounded
graphs. These automata naturally accept the same languages as the linearly
bounded machines defining them. We present some of their structural properties
as well as alternative characterizations in terms of rewriting systems and
context-sensitive transductions. Finally, we compare these graphs to rational
graphs, which are another class of automata accepting the context-sensitive
languages, and prove that in the bounded-degree case, rational graphs are a
strict sub-class of linearly bounded graphs
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