Circuit Complexity of Shuffle
We show that Shuffle(x,y,w), the problem of determining whether a string w can be composed from an order preserving shuffle of strings x and y, is not in AC0, but it is in AC1. The fact that shuffle is not in AC0 is shown by a reduction of parity to shuffle and invoking the seminal result [FSS84, while the fact that it is in AC1 is implicit in the results of [Man82a]. Together, the two results provide a strong complexity bound for this combinatorial problem.
KeywordsString shuffle circuit complexity lower bounds
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- [BS13]Buss, S.R., Soltys, M.: Unshuffling a square is NP-hard (submitted for publication, March 2013)Google Scholar
- [BTV07]Bourke, C., Tewari, R., Vinodchandran, N.V.: Directed planar reachability is in unambiguous log-space. In: Proceedings of IEEE Conference on Computational Complexity CCC (2007)Google Scholar
- [ORR78]Ogden, W.F., Riddle, W.E., Rounds, W.C.: Complexity of expressions allowing concurrency. In: Proc. 5th ACM Symposium on Principles of Programming Languages (POPL), pp. 185–194 (1978)Google Scholar
- [Pap94]Papadimitriou, C.H.: Computational Complexity. Addison-Wesley (1994)Google Scholar
- [Sho02]Shoudai, T.: A P-complete language describable with iterated shuffle. Information Processing Letters 41(5), 233–238, 1002Google Scholar
- [Sip06]Sipser, M.: Introduction to the Theory of Computation, 2nd edn. Thompson (2006)Google Scholar
- [Sol09]Soltys, M.: An introduction to computational complexity. Jagiellonian University Press (2009)Google Scholar
- [SP95]Schöning, U., Pruim, R.: Gems of Theoretical Computer Science. Springer (1995)Google Scholar