Class Of Linear Context-free Languages Research Articles

Quasi-deterministic 5' -> 3' Watson-Crick Automata

Watson-Crick (WK) finite automata are working on a Watson-Crick tape, that is, on a DNA molecule. A double stranded DNA molecule contains two strands, each having a 5' and a 3' end, and these two strands together form the molecule with the following properties. The strands have the same length, their 5' to 3' directions are opposite, and in each position, the two strands have nucleotides that are complement of each other (by the Watson-Crick complementary relation). Consequently, WK automata have two reading heads, one for each strand. In traditional WK automata both heads read the whole input in the same physical direction, but in 5'->3' WK automata the heads start from the two extremes and read the input in opposite direction. In sensing 5'->3' WK automata, the process on the input is finished when the heads meet, and the model is capable to accept the class of linear context-free languages. Deterministic variants are weaker, the class named 2detLIN, a proper subclass of linear languages is accepted by them. Recently, another specific variants, the state-deterministic sensing 5'->3' WK automata are investigated in which the graph of the automaton has the special property that for each node of the graph, all out edges (if any) go to a sole node, i.e., for each state there is (at most) one state that can be reached by a direct transition. It was shown that this concept is somewhat orthogonal to the usual concept of determinism in case of sensing 5'->3' WK automata. In this paper a new concept, the quasi-determinism is investigated, that is in each configuration of a computation (if it is not finished yet), the next state is uniquely determined although the next configuration may not be, in case various transitions are enabled at the same time. We show that this new concept is a common generalisation of the usual determinism and the state-determinism, i.e., the class of quasi-deterministic sensing 5'->3' WK automata is a superclass of both of the mentioned other classes. There are various usual restrictions on WK automata, e.g., stateless or 1-limited variants. We also prove some hierarchy results among language classes accepted by various subclasses of quasi-deterministic sensing 5'->3' WK automata and also some other already known language classes.

A note on the class of languages generated by F-systems over regular languages

An F-system is a computational model that performs a folding operation on words of a given language, following directions coded on words of another given language. This paper considers the case in which both given languages are regular, and it shows that the class of languages generated by such F-systems is a proper subset of the class of linear context-free languages.

On deterministic sensing $$5'\rightarrow 3'$$ Watson–Crick finite automata: a full hierarchy in 2detLIN

Watson–Crick (abbreviated as WK) finite automata are working on double stranded DNA molecule that is also called Watson–Crick tape. Subsequently, these automata have two reading heads, one for each strand. While in traditional WK automata both heads read the whole input in the same physical direction, in $$5'\rightarrow 3'$$ WK automata the heads start from the two extremes (say $$5'$$ end of the strands) and read the input in opposite direction. In sensing $$5'\rightarrow 3'$$ WK automata the process on the input is finished when the heads meet. Since the heads of a WK automaton may read longer strings in a transition, in previous models a so-called sensing parameter took care for the proper meeting of the heads (not allowing to read the same positions of the input in the last step). Recently a new model is investigated, which works without the sensing parameter. In this paper, the deterministic counterpart is studied and is proven to accept the language class 2detLIN defined by the deterministic variant of the earlier version. However, using some of the restricted variants, e.g, all-final automata, the classes of the accepted languages are changed showing a finer hierarchy inside the class of linear context-free languages.

Two complementary operations inspired by the DNA hairpin formation: Completion and reduction

We consider two complementary operations: Hairpin completion introduced in [D. Cheptea, C. Martin-Vide, V. Mitrana, A new operation on words suggested by DNA biochemistry: Hairpin completion, in: Proc. Transgressive Computing, 2006, pp. 216–228] with motivations coming from DNA biochemistry and hairpin reduction as the inverse operation of the hairpin completion. Both operations are viewed here as formal operations on words and languages. We settle the closure properties of the classes of regular and linear context-free languages under hairpin completion in comparison with hairpin reduction. While the class of linear context-free languages is exactly the weak-code image of the class of the hairpin completion of regular languages, rather surprisingly, the weak-code image of the class of the hairpin completion of linear context-free languages is a class of mildly context-sensitive languages. The closure properties with respect to the hairpin reduction of some time and space complexity classes are also studied. We show that the factors found in the general cases are not necessary for regular and context-free languages. This part of the paper completes the results given in the earlier paper, where a similar investigation was made for hairpin completion. Finally, we briefly discuss the iterated variants of these operations.

Nonuniform complexity and the randomness of certain complete languages

This paper contains further study of the randomness properties of languages. The connection between time-/space-bounded Kolmogorov complexity and nonuniform complexity defined by grammar and automaton size is investigated. We show that certain languages that are complete under nonuniform one-way log-space reductions are weakly random with respect to other language classes contained in P. For example, it is shown that every context-free language that is complete under nonuniform one-way log-space reductions is weakly random with respect to the class of deterministic context-free languages, and every deterministic context-free language that is complete under nonuniform one-way log-space reductions is weakly random with respect to the class of linear context-free languages.

On the intersection of the class of linear context-free languages and the class of single-reset languages

We show that so-called deterministic even linear simple matrix grammars can be inferred in polynomial time using the query-based learner–teacher model (minimally adequate teacher-learning model) proposed by Angluin (Inform. and Comput. 75 (1987) 87) for learning deterministic regular languages. In this way, we extend the class of efficiently learnable languages beyond both the even linear languages and the even equal matrix languages (Pattern Recognition 21 (1988) 55; Proc. 2nd Internat. Colloq. on Grammatical Inference (ICGI-94): Grammatical Inference and Applications, Lecture Notes in Computer Science/Lecture Notes in Artificial Intelligence, vol. 862, Springer, Berlin, 1994, p. 38; Inform. Process. Lett. 28 (1988) 193; Technical Report IIAS-RR-93-6E, Fujitsu Laboratories, 1992; Parallel Image Analysis, ICPIA’92, Lecture Notes in Computer Science, vol. 652, Springer, Berlin, 1992, p. 274; Inform. and Comput. 123 (1995) 138; Algorithmic Learning for Knowledge-Based Systems, Lecture Notes in Computer Science/Lecture Notes in Artificial Intelligence, Springer, Berlin, 1995, p. 317). Moreover, we investigate formal language properties of even linear simple matrix languages and related language classes. More precisely, we discuss characterizations, (proper) inclusion relations, closure properties and decidability questions. This way, we also show that, in a certain sense, the idea of iterating the control language approach for learning purposes, as undertook by Takada (1995), could be seen as a special case of using deterministic even linear simple matrix grammars as basic and uniform learning target.

A machine realization of the linear context-free languages

A correspondence is established between N 2 , the class of sets of pairs of tapes defined by nondeterministic 2-tape finite automata, and L , the class of linear context-free languages. A second correspondence, which is one-one, between N 2 and a subclass of L is found. This subclass of L is then characterized by expressions quite similar to regular expressions. It is indicated how to develop analogous characterizations for other subclasses of L . A large portion of this paper appears in the author's doctoral thesis which was presented to the Division of Engineering and Applied Physics, Harvard University. The thesis research was under the supervision of Professor Patrick C. Fischer.

Inherent ambiguity of minimal linear grammars

We give an example of minimal linear language, all of whose minimal linear grammars are ambiguous; this language is not ambiguous in the class of linear context-free languages.