10,597 research outputs found
Time-Bounded Controlled Bidirectional Grammars
We study regularly controlled bidirectional (RCB) grammars from the viewpoint of time-bounded grammars. RCB-grammars are context-free grammars of which the rules can be used in a productive and in a reductive fashion, while the application of these rules is controlled by a regular language. Several modes of derivation can be distinguished for this kind of grammar. A time-bound on such a grammar is a measure of its derivational complexity. For some families of time bounds and for some modes of derivation we establish closure properties and a normal form theorem. In addition parsing algorithms are given for some modes of derivation. We conclude with considering generalizations with respect to the family of control languages and the family of bounding functions
Capacity Bounded Grammars and Petri Nets
A capacity bounded grammar is a grammar whose derivations are restricted by
assigning a bound to the number of every nonterminal symbol in the sentential
forms. In the paper the generative power and closure properties of capacity
bounded grammars and their Petri net controlled counterparts are investigated
Complexity of Problems of Commutative Grammars
We consider commutative regular and context-free grammars, or, in other
words, Parikh images of regular and context-free languages. By using linear
algebra and a branching analog of the classic Euler theorem, we show that,
under an assumption that the terminal alphabet is fixed, the membership problem
for regular grammars (given v in binary and a regular commutative grammar G,
does G generate v?) is P, and that the equivalence problem for context free
grammars (do G_1 and G_2 generate the same language?) is in
Coding-theorem Like Behaviour and Emergence of the Universal Distribution from Resource-bounded Algorithmic Probability
Previously referred to as `miraculous' in the scientific literature because
of its powerful properties and its wide application as optimal solution to the
problem of induction/inference, (approximations to) Algorithmic Probability
(AP) and the associated Universal Distribution are (or should be) of the
greatest importance in science. Here we investigate the emergence, the rates of
emergence and convergence, and the Coding-theorem like behaviour of AP in
Turing-subuniversal models of computation. We investigate empirical
distributions of computing models in the Chomsky hierarchy. We introduce
measures of algorithmic probability and algorithmic complexity based upon
resource-bounded computation, in contrast to previously thoroughly investigated
distributions produced from the output distribution of Turing machines. This
approach allows for numerical approximations to algorithmic
(Kolmogorov-Chaitin) complexity-based estimations at each of the levels of a
computational hierarchy. We demonstrate that all these estimations are
correlated in rank and that they converge both in rank and values as a function
of computational power, despite fundamental differences between computational
models. In the context of natural processes that operate below the Turing
universal level because of finite resources and physical degradation, the
investigation of natural biases stemming from algorithmic rules may shed light
on the distribution of outcomes. We show that up to 60\% of the
simplicity/complexity bias in distributions produced even by the weakest of the
computational models can be accounted for by Algorithmic Probability in its
approximation to the Universal Distribution.Comment: 27 pages main text, 39 pages including supplement. Online complexity
calculator: http://complexitycalculator.com
On the generating power of regularly controlled bidirection grammars
RCB-grammars or regularly controlled bidirectional grammars are context-free grammars of which the rules can be used in a productive and in a reductive fashion. In addition, the application of these\ud
rules is controlled by a regular language. Several modes of derivation can be distinguished for this kind of grammar. In this paper the generating power of the derivation mode that uses right-occurrence rewriting (RO-mode) is determined. Furthermore, a new mode called RA is introduced, which is a better formalization of the intuitive idea of rightoccurrence rewriting than the RO-mode. The RO- and RA-mode have the same generating power, viz. the corresponding RCB-grammars both generate the recursively enumerable languages. Consequently, providing RCB/RO-grammars with a time bound results in a less powerful grammar model
On the Generating Power of Regularly Controlled Bidirectional Grammars
RCB-grammars or regularly controlled bidirectional grammars are context-free grammars of which the rules can be used in a productive and in a reductive fashion. In addition, the application of these rules is controlled by a regular language. Several modes of derivation can be distinguished for this kind of grammar. In this paper the generating power of the derivation mode that uses right-occurrence rewriting (RO-mode) is determined. Furthermore, a new mode called RA is introduced, which is a better formalization of the intuitive idea of right-occurrence rewriting than the RO-mode. The RO- and RA-mode have the same generating power, viz. the corresponding RCB-grammars both generate the recursively enumerable languages. Consequently, providing RCB/RO-grammars with a time bound results in a less powerful grammar model
Extended macro grammars and stack controlled machines
K-extended basic macro grammars are introduced, where K is any class of languages. The class B(K) of languages generated by such grammars is investigated, together with the class LB(K) of languages generated by the corresponding linear basic grammars. For any full semi-AFL K, B(K) is a full AFL closed under iterated LB(K)-substitution, but not necessarily under substitution. For any machine type D, the stack controlled machine type corresponding to D is introduced, denoted S(D), and the checking-stack controlled machine type CS(D). The data structure of this machine is a stack which controls a pushdown of data structures from D. If D accepts K, then S(D) accepts B(K) and CS(D) accepts LB(K). Thus the classes B(K) are characterized by stack controlled machines and the classes LB(K), i.e., the full hyper-AFLs, by checking-stack controlled machines. A full basic-AFL is a full AFL K such that B(K)C K. Every full basic-AFL is a full hyper-AFL, but not vice versa. The class of OI macro languages (i.e., indexed languages, i.e., nested stack automaton languages) is a full basic-AFL, properly containing the smallest full basic-AFL. The latter is generated by the ultrabasic macro grammars and accepted by the nested stack automata with bounded depth of nesting (and properly contains the stack languages, the ETOL languages, i.e., the smallest full hyper-AFL, and the basic macro languages). The full basic-AFLs are characterized by bounded nested stack controlled machines
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
Tightening the Complexity of Equivalence Problems for Commutative Grammars
We show that the language equivalence problem for regular and context-free
commutative grammars is coNEXP-complete. In addition, our lower bound
immediately yields further coNEXP-completeness results for equivalence problems
for communication-free Petri nets and reversal-bounded counter automata.
Moreover, we improve both lower and upper bounds for language equivalence for
exponent-sensitive commutative grammars.Comment: 21 page
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