Abstract
We develop a behavioural theory of reflective sequential algorithms (RSAs), i.e. algorithms that can modify their own behaviour. The theory comprises a set of language-independent postulates characterising the class of RSAs, an abstract machine model that provably satisfies the postulates, and a proof that all RSAs are captured by this machine model. As in Gurevich’s thesis for sequential algorithms RSAs are sequential-time, bounded parallel algorithms, where the bound depends on the algorithm only and not on the input. Different from the class of sequential algorithms every state of an RSA includes a representation of the algorithm in that state, thus enabling linguistic reflection. The model of reflective Abstract State Machines (rASMs) extends sequential ASMs using extended states that include an updatable representation of the main ASM rule to be executed by the machine in that state.
The research reported in this paper results from the projects Behavioural Theory and Logics for Distributed Adaptive Systems and Higher-Order Logics and Structure supported by the Austrian Science Fund (FWF: [P26452-N15] & [I2420-N31]).
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Notes
- 1.
As usual, \(val_S(t)\) denotes the interpretation of a ground term t as a value in the base set of a state S.
- 2.
Two sequential algorithms \(P_1\) and \(P_2\) are behavioural equivalent if \(\mathcal{S}_{P_1} = \mathcal{S}_{P_2}\), \(\mathcal{I}_{P_1} = \mathcal{I}_{P_2}\) and \(\tau _{P_1} = \tau _{P_2}\). Behavioural equivalent sequential algorithms have the same runs.
References
Blass, A., Gurevich, Y.: Abstract state machines capture parallel algorithms. ACM Trans. Comput. Logic 4(4), 578–651 (2003)
Blass, A., Gurevich, Y.: Abstract state machines capture parallel algorithms: correction and extension. ACM Trans. Comp. Logic 9(3), 19 (2008)
Börger, E.: The ASM refinement method. Formal Aspects Comput. 15, 237–257 (2003)
Börger, E., Schewe, K.D.: Concurrent abstract state machines. Acta Inform. 53(5), 469–492 (2016)
Börger, E., Stärk, R.: Abstract State Machines. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-642-18216-7
Ferrarotti, F., Schewe, K.D., Tec, L., Wang, Q.: A new thesis concerning synchronised parallel computing - simplified parallel ASM thesis. Theor. Comput. Sci. 649, 25–53 (2016)
Ferrarotti, F., Tec, L., Torres, J.M.T.: Towards an ASM thesis for reflective sequential algorithms. In: Butler, M., Schewe, K.-D., Mashkoor, A., Biro, M. (eds.) ABZ 2016. LNCS, vol. 9675, pp. 244–249. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-33600-8_16
Gurevich, Y.: Sequential abstract-state machines capture sequential algorithms. ACM Trans. Comput. Logic 1(1), 77–111 (2000)
Riccobene, E., Scandurra, P.: Towards ASM-based formal specification of self-adaptive systems. In: Ameur, Y.A., Schewe, K.D. (eds.) Abstract State Machines, Alloy, B, TLA, VDM, and Z. LNCS, vol. 8477, pp. 204–209. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-43652-3
Schewe, K.D., Wang, Q.: A customised ASM thesis for database transformations. Acta Cybern. 19(4), 765–805 (2010)
Smith, B.C.: Reflection and semantics in LISP. In: Proceedings of the 11th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, POPL 1984, pp. 23–35. ACM (1984)
Stemple, D., et al.: Type-safe linguistic reflection: a generator technology. In: Atkinson, M., Welland, R. (eds.) Fully Integrated Data Environments. Esprit Basic Research Series, pp. 158–188. Springer, Heidelberg (2000). https://doi.org/10.1007/978-3-642-59623-0_8
Van den Bussche, J., Van Gucht, D., Vossen, G.: Reflective programming in the relational algebra. J. Comput. Syst. Sci. 52(3), 537–549 (1996)
Wang, Q., Ferrarotti, F., Schewe, K.D., Tec, L.: A complete logic for non-deterministic database transformations. CoRR abs/1602.07486 (2016). http://arxiv.org/abs/1602.07486
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Ferrarotti, F., Schewe, KD., Tec, L. (2018). A Behavioural Theory for Reflective Sequential Algorithms. In: Petrenko, A., Voronkov, A. (eds) Perspectives of System Informatics. PSI 2017. Lecture Notes in Computer Science(), vol 10742. Springer, Cham. https://doi.org/10.1007/978-3-319-74313-4_10
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