Abstract
We look at NFAs augmented with multiple reversal-bounded counters where, during an accepting computation, the behavior of the counters during increasing and decreasing phases is specified by some fixed “pattern”. We consider families of languages defined by various pattern behaviors and show that some correspond to the smallest full trios containing restricted classes of bounded semilinear languages. For example, one such family is exactly the smallest full trio containing all the bounded semilinear languages. Another family is the smallest full trio containing all the bounded context-free languages. Still another is the smallest full trio containing all bounded languages whose Parikh map is a semilinear set where all periodic vectors have at most two non-zero coordinates. We also examine relationships between the families.
The research of O. H. Ibarra was supported, in part, by NSF Grant CCF-1117708. The research of I. McQuillan was supported, in part, by Natural Sciences and Engineering Research Council of Canada Grant 327486-2010.
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Notes
- 1.
There is a fixed c such that the number of times the boundary between any two adjacent input cells is crossed is at most c.
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Ibarra, O.H., McQuillan, I. (2016). On Families of Full Trios Containing Counter Machine Languages. In: Brlek, S., Reutenauer, C. (eds) Developments in Language Theory. DLT 2016. Lecture Notes in Computer Science(), vol 9840. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53132-7_18
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