Formal languages
Parallel parsing on a one-way linear array of finite-state machines
Theoretical Computer Science
An Infinite Hierarchy of Context-Free Languages
Journal of the ACM (JACM)
Regular Closure of Deterministic Languages
SIAM Journal on Computing
Automata arrays and context-free languages
Where mathematics, computer science, linguistics and biology meet
Introduction to Formal Language Theory
Introduction to Formal Language Theory
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Journal of Computer and System Sciences
Real-time language recognition by one-dimensional cellular automata
Journal of Computer and System Sciences
On Extended Regular Expressions
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Linear conjunctive grammars and one-turn synchronized alternating pushdown automata
FG'09 Proceedings of the 14th international conference on Formal grammar
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Turn bounded pushdown automata with different conditions for beginning a new turn are investigated. Their relationships with closures of the linear context-free languages under regular operations are studied. For example, automata with an unbounded number of turns that have to empty their pushdown store up to the initial symbol in order to start a new turn are characterized by the regular closure of the linear languages. Automata that additionally have to re-enter the initial state are (almost) characterized by the Kleene star closure of the linear languages. For both a bounded and an unbounded number of turns, requiring to empty the pushdown store is a strictly stronger condition than requiring to re-enter the initial state. Several new language families are obtained which form a double-stranded hierarchy. Closure properties of these families under AFL operations are derived. The regular closure of the linear languages share the strong closure properties of the context-free languages, i.e., the family is a full AFL. Interestingly, three natural new language families are not closed under intersection with regular languages and inverse homomorphism. Finally, an algorithm is presented parsing languages from the new families in quadratic time.