Abstract
Reversible circuits provide the subject of a new promising direction of circuit design. Reversible circuits are cascades of reversible gates specifying bijective functions on Boolean vectors. As one encounters quite a variety of reversible gates in the literature, there are many classes of reversible circuits. Two main problems are considered: (1) How can circuits of one class be transformed into the ones of another class? (2) How can circuits within one class be optimized with respect to certain measures? While reversible circuits are studied on the functional level and on the level of propositional calculus, there is also a visual representation used frequently for illustrative purposes in an informal way. In this paper, the visual description of reversible circuits is formalized by means of graph transformation. In particular, it is shown that the problems of model transformation and optimization can be investigated within the graph-transformational framework. This continues the authors’ earlier work on the generation, evaluation and synthesis of reversible circuits as graphs.
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References
Toffoli, T.: Reversible computing. In: de Bakker, J., van Leeuwen, J. (eds.) Automata, Languages and Programming. LNCS, pp. 632–644. Springer, Heidelberg (1980)
Fredkin, E., Toffoli, T.: Conservative logic. Int. J. Theor. Phys. 21(3/4), 219–253 (1982)
Kreowski, H.-J., Kuske, S., Lye, A., Luderer, M.: Graph transformation meets reversible circuits: generation, evaluation, and synthesis. In: Giese, H., König, B. (eds.) ICGT 2014. LNCS, vol. 8571, pp. 237–252. Springer, Heidelberg (2014)
Maslov, D., Dueck, G.W., Michael Miller, D.: Toffoli network synthesis with templates. IEEE Trans. Comput. Aided Des. Integr. Circ. Syst. 24(6), 807–817 (2005)
Arabzadeh, M., Saeedi, M., Zamani, M.S.: Rule-based optimization of reversible circuits. In: Proceedings of 15th Asia South Pacific Design Automation Conference, ASP-DAC 2010, pp. 849–854. IEEE (2010)
Soeken, M., Thomsen, M.K.: White dots do matter: rewriting reversible logic circuits. In: Dueck, G.W., Miller, D.M. (eds.) RC 2013. LNCS, vol. 7948, pp. 196–208. Springer, Heidelberg (2013)
Thomsen, M.K., Kaarsgaard, R., Soeken, M.: Ricercar: a language for describing and rewriting reversible circuits with ancillae and its permutation semantics. In: Krivine, J., Stefani, J.B. (eds.) Reversible Computation. LNCS, vol. 9138, pp. 200–215. Springer, Switzerland (2015)
Kreowski, H.-J., Klempien-Hinrichs, R., Kuske, S.: Some essentials of graph transformation. In: Esik, Z., Martín-Vide, C., Mitrana, V. (eds.) Recent Advances in Formal Languages and Applications. SCI, vol. 25, pp. 229–254. Springer, Heidelberg (2006)
Courcelle, B., Engelfriet, J.: Graph Structure and Monadic Second-Order Logic - A Language-Theoretic Approach. Cambridge University Press, Cambridge (2012)
Kreowski, H.-J., Kuske, S., Lye, A.: Canonical multi-target toffoli circuits. In: Dediu, A.H., et al. (eds.) LATA 2016. LNCS, vol. 9618, pp. 603–616. Springer, Heidelberg (2016). doi:10.1007/978-3-319-30000-9_46
Saeedi, M., Wille, R., Drechsler, R.: Synthesis of quantum circuits for linear nearest neighbor architectures. Quantum Inf. Process. 10(3), 355–377 (2011)
Lye, A., Wille, R., Drechsler, R.: Determining the minimal number of swap gates for multi-dimensional nearest neighbor quantum circuits. In: Proceedings of 20th Asia and South Pacific Design Automation Conference, ASP-DAC 2015, pp. 178–183. IEEE (2015)
Drewes, F., Habel, A., Kreowski, H.-J.: Hyperedge replacement graph grammars. In: Rozenberg, G. (ed.) Handbook of Graph Grammars and Computing by Graph Transformation: Foundations, vol. 1, pp. 95–162. World Scientific, Singapore (1997)
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We are greatful to the anonymous reviewers for their valuable comments that led to various improvements.
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Kreowski, HJ., Kuske, S., Lye, A., von Totth, C. (2016). Graph Transformation Meets Reversible Circuits: Model Transformation and Optimization. In: Echahed, R., Minas, M. (eds) Graph Transformation. ICGT 2016. Lecture Notes in Computer Science(), vol 9761. Springer, Cham. https://doi.org/10.1007/978-3-319-40530-8_15
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DOI: https://doi.org/10.1007/978-3-319-40530-8_15
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