Growing context-sensitive languages and Church-Rosser languages
Gerhard Buntrock,Friedrich Otto +1 more
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TLDR
The class of (generalized) Church-Rosser languages and the class of context-free languages are incomparable under set inclusion, which verifies a conjecture of Mc-Naughton et al [MNO88].Abstract:
The growing context-sensitive languages (GCSL) are characterized by a nondeterministic machine model, the so-called shrinking two-pushdown automaton (sTPDA). Then the deterministic version of this automaton (sDTPDA) is shown to characterize the class of generalized Church-Rosser languages (GCRL). Finally, we prove that each growing context-sensitive language is accepted in polynomial time by some one-way auxiliary pushdown automaton with a logarithmic space bound (OW-auxPDA[log, poly]). As a consequence the class of (generalized) Church-Rosser languages and the class of context-free languages are incomparable under set inclusion, which verifies a conjecture of Mc-Naughton et al [MNO88].read more
Citations
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Journal ArticleDOI
Complexity of multi-head finite automata: Origins and directions
TL;DR: A tour of a vast literature on computational and descriptional complexity issues on multi-head finite automata documenting the importance of these devices and the borderline between decidable and undecidable problems is toured.
Journal ArticleDOI
The Church-Rosser languages are the deterministic variants of the growing context-sensitive languages
Gundula Niemann,Friedrich Otto +1 more
TL;DR: It is shown that shrinking two-pushdown automata and length-reducing two- pushing down automata are equivalent, both in the non-deterministic and the deterministic case, thus obtaining still another characterization of the growing context-sensitive languages and the Church-Rosser languages, respectively.
Book ChapterDOI
Restarting automata and their relations to the Chomsky hierarchy
TL;DR: A survey on the various models and their properties is given, their relationships to the language classes of the Chomsky hierarchy are described, and some open problems are presented as mentioned in this paper, where the authors present a set of open problems.
Journal ArticleDOI
On stateless two-pushdown automata and restarting automata
TL;DR: Various types of stateless two-pushdown automata and restarting automata are considered and their expressive power is investigated, comparing them in particular to each other and to the corresponding types of automata with states.
Journal ArticleDOI
Shrinking restarting automata
Tomasz Jurdziński,Friedrich Otto +1 more
TL;DR: A natural generalization of this model, called shrinking restarting automaton, where it is only required that there exists a weight function such that each rewrite step decreases the weight of the tape content with respect to that function.
References
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Book
Introduction to Automata Theory, Languages, and Computation
TL;DR: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
Journal ArticleDOI
Semantics of context-free languages
TL;DR: The implications of this process when some of the attributes of a string are “synthesized”, i.e., defined solely in terms of attributes of thedescendants of the corresponding nonterminal symbol, while other attributes are ‘inherited’, are examined.
Book
String-rewriting systems
Ronald V. Book,Friedrich Otto +1 more
TL;DR: This chapter provides formal definitions of string-rewriting systems and their induced reduction relations and Thue congruences and relies on Section 1.4 for basic definitions and notation for strings.
Journal ArticleDOI
Tree-size bounded alternation
TL;DR: In this paper, the size of an accepting computation tree of an alternating Turing machine (ATM) is introduced as a complexity measure, and a number of applications of tree-size to the study of more traditional complexity classes are presented.
Journal ArticleDOI
On the Tape Complexity of Deterministic Context-Free Languages
TL;DR: A tape hardest deterministic context-free language is described and the best upper bound known on the tape complexity of (deterministic) context- free languages is (log(n) 2).
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