Automata play important roles in wide area of computing and the growth of multicores calls for their efficient parallel implementation. Though it is known in theory that we can perform theâ€¦ (More)

An abstract numeration system (ANS) is a numeration system that provides a one-to-one correspondence between the natural numbers and a regular language. In this paper, we define an ANS-basedâ€¦ (More)

A zero-one language L is a regular language whose asymptotic probability converges to either zero or one. In this case, we say that L obeys the zero-one law. We prove that a regular language obeysâ€¦ (More)

It is well known that the length of a Î²-reduction sequence of a simply typed Î»-term of order k can be huge; it is as large as k-fold exponential in the size of the Î»-term in the worst case. Weâ€¦ (More)

It is well known that the length of a Î²-reduction sequence of a simply typed Î»-term of order k can be huge; it is as large as k-fold exponential in the size of the Î»-term in the worst case. Weâ€¦ (More)

The automaton constrained tree knapsack problem is a variant of the knapsack problem in which the items are associated with the vertices of the tree, and we can select a subset of items that isâ€¦ (More)

A regular language has the zero-one law if its asymptotic density converges to either zero or one. We prove that the class of all zero-one languages is closed under Boolean operations and quotients.â€¦ (More)

We prove that a minimal automaton has a minimal adjacency matrix rank and a minimal adjacency matrix nullity using equitable partition (from graph spectra theory) and Nerode partition (from automataâ€¦ (More)