In this paper, the space complexity of nonuniform quantum algorithms is investigated using the model of quantum branching programs (QBPs). In order to clarify the relationship between QBPs and nonuniform quantum Turing machines, simulations between these two models are presented which allow to transfer upper and lower bound results. Exploiting additional insights about the connection between the running time and the precision of amplitudes, it is shown that nonuniform quantum Turing machines with algebraic amplitudes and QBPs with a suitable analogous set of amplitudes are equivalent in computational power if both models work with bounded or unbounded error. Furthermore, quantum ordered binary decision diagrams (QOBDDs) are considered, which are restricted QBPs that can be regarded as a nonuniform analog of one-way quantum finite automata. Upper and lower bounds are proved that allow a classification of the computational power of QOBDDs in comparison to usual deterministic and randomized variants of the model. Finally, an extension of QBPs is proposed where the performed unitary operation may depend on the result of a previous measurement. A simulation of randomized BPs by this generalized QBP model as well as exponential lower bounds for its ordered variant are presented.

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On the complexity of the hidden weighted bit function for various BDD models Informatique théorique et applications, tome 33, n o 2 (1999), p. 103-115 © AFCET, 1999, tous droits réservés. L'accès aux archives de la revue « Informatique théorique et applications » implique l'accord avec les conditions générales d'utilisation (http://www.numdam. org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Theoretical Informaties and Applications

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The problem to construct an OBDD cover of minimal size for an incompletely speci ed Boolean function arises in several applications in the CAD domain, e. g. the veri cation of sequential machines and the construction of OBDDs for incompletely speci ed circuits. The complexity of this problem is determined. The decision problem is NP{complete. E cient approximation algorithms exist only if NP=P.