Journal ArticleDOI
Computational Complexity of Certain Problems Related to Carefully Synchronizing Words for Partial Automata and Directing Words for Nondeterministic Automata
TLDR
It is shown that the problem of checking careful synchronizability of partial finite automata is PSPACE-complete and the problems of checking D1, D2, and D3-directability of nondeterministic finite Automata are PSPACE -complete.Citations
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Book
Algebraic theory of automata and languages
TL;DR: Some operations on languages and special classes of regular languages associated with deterministic and nondeterministic directable automata are dealt with and automorphism groups of automata and the partially ordered sets of Automata are systematically discussed.
Book ChapterDOI
On Two Algorithmic Problems about Synchronizing Automata
TL;DR: In this paper, it was shown that two natural problems from the theory of synchronizing automata cannot be solved in polynomial time under the assumption that P≠NP.
Posted Content
Primitive sets of nonnegative matrices and synchronizing automata
TL;DR: In this article, it was shown that the maximal exponent of a set of matrices having total support is bounded by 2n 2 -5n +5 n +5, which leads to a resolution of the Cerný problem for carefully synchronizing automata.
Journal ArticleDOI
Primitive Sets of Nonnegative Matrices and Synchronizing Automata
TL;DR: The present paper provides equivalence results about primitive sets of matrices without zero rows and columns, denoted by $\mathscr{NZ}$, due to its intriguing connections to the Cerný conjecture.
Book ChapterDOI
Synchronizing Strategies under Partial Observability
TL;DR: This work extends the existing theory of synchronizing words to synchronizing strategies, and study the synchronization, short-synchronization and subset-to-subset synchronization problems under partial observability, concluding that for deterministic systems the complexity of the problems underpartial observability remains the same as for the classical synchronization problems.
References
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Journal ArticleDOI
Relationships between nondeterministic and deterministic tape complexities
TL;DR: The amount of storage needed to simulate a nondeterministic tape bounded Turingmachine on a deterministic Turing machine is investigated and a specific set is produced, namely the set of all codings of threadable mazes, such that, if there is any set which distinguishes nondeter microscopic complexity classes from deterministic tape complexity classes, then this is one such set.
Proceedings ArticleDOI
Lower bounds for natural proof systems
TL;DR: A lower space bound of n/log(n) is shown for the proof system for the PTIME complete theory and a lower length bound of 2cn/log('n'): length of polynomial space for the PSPACE complete theory.
Book ChapterDOI
Synchronizing Automata and the Černý Conjecture
TL;DR: Some recent advances towards a solution of the Cerný conjecture are discussed and several results and open problems related to synchronizing automata are surveyed.
Journal ArticleDOI
Reset sequences for monotonic automata
TL;DR: A new algorithm based on breadth-first search is presented that runs in faster asymptotic time than Natarajan’s algorithms, and in addition finds the shortest possible reset sequence if such a sequence exists.