Abstract
Alon et al. (SICOMP 2001) showed that all regular languages are testable with a constant number of queries. On the other hand, they also showed that some context free languages require \(\Omega(\sqrt{n})\) queries to test. Following this, Alon et al. suggested the problem of classifying the context free languages that are testable with a constant number of queries.
We make progress towards the solution of this problem. Our main result is that languages accepted by weak counter automata are testable with a constant number of queries. A counter automaton is a pushdown automaton with a single stack symbol, effectively a non-negative counter that the automaton may compare to zero. It is weak if the set of possible transitions with a zero counter is a subset of the possible transitions with a positive counter. Note that this restriction is essential, since Lachish et. al. (CC 2008) proved that there exist counter automaton languages requiring Ω(polylog n) queries to test.
The research leading to these results has received funding from the European Union’s - Seventh Framework Programme [FP7/2007-2013] under grant agreement no. 202405 (PROPERTY TESTING).
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Goldhirsh, Y., Viderman, M. (2013). Testing Membership in Counter Automaton Languages. In: Raghavendra, P., Raskhodnikova, S., Jansen, K., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2013 2013. Lecture Notes in Computer Science, vol 8096. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40328-6_38
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DOI: https://doi.org/10.1007/978-3-642-40328-6_38
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