Models of multi-output and scalar recursive Boolean circuits of bounded depth in an arbitrary basis are considered. Methods for lower and upper estimates for the Shannon function for the complexity of circuits of these classes are provided. Based on these methods, an asymptotic formula for the Shannon function is put forward. Moreover, in the above classes of recursive circuits, upper estimates for the complexity of implementation of some functions and systems of functions used in applications are obtained.

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Context. As part of our international program aimed at obtaining accurate physical properties of trans-Neptunian objects (TNOs), we predicted a stellar occultation by the TNO (38628) Huya of the star Gaia DR2 4352760586390566400 (mG = 11.5 mag) on March 18, 2019. After an extensive observational campaign geared at obtaining the astrometric data, we updated the prediction and found it favorable to central Europe. Therefore, we mobilized half a hundred of professional and amateur astronomers in this region and the occultation was finally detected by 21 telescopes located at 18 sites in Europe and Asia. This places the Huya event among the best ever observed stellar occultation by a TNO in terms of the number of chords. Aims. The aim of our work is to determine an accurate size, shape, and geometric albedo for the TNO (38628) Huya by using the observations obtained from a multi-chord stellar occultation. We also aim to provide constraints on the density and other internal properties of this TNO. Methods. The 21 positive detections of the occultation by Huya allowed us to obtain well-separated chords which permitted us to fit an ellipse for the limb of the body at the moment of the occultation (i.e., the instantaneous limb) with kilometric accuracy. Results. The projected semi-major and minor axes of the best ellipse fit obtained using the occultation data are (a′, b′) = (217.6 ± 3.5 km, 194.1 ± 6.1 km) with a position angle for the minor axis of P′ = 55.2° ± 9.1. From this fit, the projected area-equivalent diameter is 411.0 ± 7.3 km. This diameter is compatible with the equivalent diameter for Huya obtained from radiometric techniques (D = 406 ± 16 km). From this instantaneous limb, we obtained the geometric albedo for Huya (pV = 0.079 ± 0.004) and we explored possible three-dimensional shapes and constraints to the mass density for this TNO. We did not detect the satellite of Huya through this occultation, but the presence of rings or debris around Huya was constrained using the occultation data. We also derived an upper limit for a putative Pluto-like global atmosphere of about psurf = 10 nbar.

We introduce the notion of reflexive-recursive circuits and consider classes of many-output and scalar reflexive-recursive circuits of bounded depth in an arbitrary basis. Methods are proposed for deriving lower and upper bounds on the Shannon function for the complexity of circuits from these classes and asymptotic expressions are established. We also derive upper bounds for the realization complexity in these classes of circuits for some functions and systems of functions occurring in applications.

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