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Let Σ be a finite alphabet, Σ* the free monoid generated by Σ and |x| the length of x ε Σ*. For any integer k ≥ 0, fk(x)(tk (x)) is x if |x| ≪ k+1, and it is the prefix (suffix) of x of length k, otherwise. Also let mk+1 (x) = {v|x = uvw and |v| = k+1}. For x,y ε Σ* define x ∼k+1y iff fk(x) = fk(y), tk(x) = tk(y) and mk+1(x) = mk+1 (y). The relation ∼k+1 is a congruence of finite index over Σ*. An...
Certain properties of three variants of the multi-tape automata of Rabin and Scott are proved. Closure properties of the defined sets of n-tuples are found, and the nature of projections of the defined sets of n-tuples on one coordinate is studied. Some necessary conditions for acceptance are derived, and a characterization of the sets of n-tuples defined by non-deterministic n-tape automata is found...
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