On the Complexity of Free Monoid Morphisms

We locate the complexities of evaluating, of inverting, and of testing membership in the image of, morphisms h: Σ* → Δ*. By and large, we show these problems complete for classes within NL. Then we develop new properties of finite codes and of finite sets of words, which yield image membership subproblems that are closely tied to the unambiguous space classes found between L and NL.

[1]  Eric Allender,et al.  StUSPACE(log n) <= DSPACE(log²n / log log n) , 1996, ISAAC.

[2]  David A. Mix Barrington,et al.  Bounded-width polynomial-size branching programs recognize exactly those languages in NC1 , 1986, STOC '86.

[3]  Howard Straubing.  Finite Automata, Formal Logic, and Circuit Complexity , 1994, Progress in Theoretical Computer Science.

[4]  Birgit Jenner.  Knapsack Problems for NL , 1995, Inf. Process. Lett..

[5]  Samuel Eilenberg,et al.  Automata, languages, and machines. A , 1974, Pure and applied mathematics.

[6]  Marcel Paul Schützenberger,et al.  On Finite Monoids Having Only Trivial Subgroups , 1965, Inf. Control..

[7]  Wojciech Rytter.  The Space Complexity of the Unique Decipherability Problem , 1986, Inf. Process. Lett..

[8]  Neil D. Jones,et al.  Space-Bounded Reducibility among Combinatorial Problems , 1975, J. Comput. Syst. Sci..

[9]  J. Håstad.  Computational limitations of small-depth circuits , 1987 .

[10]  Eric Allender,et al.  Making nondeterminism unambiguous , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[11]  Neil Immerman,et al.  On Uniformity within NC¹ , 1990, J. Comput. Syst. Sci..

[12]  Klaus-Jörn Lange.  An Unambiguous Class Possessing a Complete Set , 1997, STACS.