Journal of the ACM (JACM)
Reversal-Bounded Multicounter Machines and Their Decision Problems
Journal of the ACM (JACM)
Symbolic String Verification: An Automata-Based Approach
SPIN '08 Proceedings of the 15th international workshop on Model Checking Software
Symbolic String Verification: Combining String Analysis and Size Analysis
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
Relational string verification using multi-track automata
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
On synchronized multitape and multihead automata
DCFS'11 Proceedings of the 13th international conference on Descriptional complexity of formal systems
Weak synchronization and synchronizability of multitape pushdown automata and turing machines
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
How to synchronize the heads of a multitape automaton
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
On the open problem of Ginsburg concerning semilinear sets and related problems
Theoretical Computer Science
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Given an n -tape nondeterministic finite automaton (NFA) M with a one-way read-only head per tape and a right end marker $ on each tape, and a nonnegative integer k , we say that M is weakly k -synchronized if for every n -tuple x =(x 1 , …, x n ) that is accepted, there is a computation on x such that at any time during the computation, no pair of input heads, neither of which is on $, are more than k cells apart. As usual, an n -tuple x =(x 1 , …, x n ) is accepted if M eventually reaches the configuration where all n heads are on $ in an accepting state. We show decidable and undecidable results concerning questions such as: (1) Given M , is it weakly k -synchronized for some k (resp., for a specified k ) and (2) Given M , is there a weakly k -synchronized M ′ for some k (resp., for a specified k ) such that L (M ′)=L (M )? Most of our results are the strongest possible in the sense that slight restrictions on the models make the undecidable problems decidable. A few questions remain open.