Natural Computing

, Volume 11, Issue 4, pp 579–594 | Cite as

Computation with multiple CTCs of fixed length and width

  • A. C. Cem SayEmail author
  • Abuzer Yakaryılmaz


We examine some variants of computation with closed timelike curves (CTCs), where various restrictions are imposed on the memory of the computer, and the information carrying capacity and range of the CTC. We give full characterizations of the classes of languages decided by polynomial time probabilistic and quantum computers that can send a single classical bit to their own past. We show that, given a time machine with constant negative delay, one can implement CTC-based computations without the need to know about the runtime beforehand. Chaining multiple instances of such fixed-length CTCs, the power of postselection can be endowed to deterministic computers, all languages in \(\mathsf{NP} \cup \mathsf{coNP}\) can be decided with no error in worst-case polynomial time, and all Turing-decidable languages can be decided in constant expected time. We provide proofs of the following facts for weaker models: Augmenting probabilistic computers with a single CTC leads to an improvement in language recognition power. Quantum computers under these restrictions are more powerful than their classical counterparts. Some deterministic models assisted with multiple CTCs are more powerful than those with a single CTC.


Closed timelike curve (CTC) CTC-based computation Postselection Polynomial-time probabilistic and quantum algorithms Probabilistic and quantum automata Deterministic pushdown automata Limited nondeterminism 



We thank David Deutsch, Scott Aaronson, Seth Lloyd, Amos Ori, Todd Brun, Taylan Cemgil, and Charles Bennett for their helpful answers and remarks. We are also grateful to all the anonymous reviewers of the past and present versions of this manuscript for their insightful comments. We were partially supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) with grant 108E142. Yakaryılmaz was also partially supported by the FP7 FET-Open project QCS.


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Computer EngineeringBoğaziçi UniversityIstanbulTurkey
  2. 2.Faculty of ComputingUniversity of LatviaRigaLatvia

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