Approaching MCSP from Above and Below: Hardness for a Conditional Variant and AC^0[p]

The Minimum Circuit Size Problem (MCSP) asks whether a given Boolean function has a circuit of at most a given size. MCSP has been studied for over a half-century and has deep connections throughout theoretical computer science including to cryptography, computational learning theory, and proof complexity. For example, we know (informally) that if MCSP is easy to compute, then most cryptography can be broken. Despite this cryptographic hardness connection and extensive research, we still know relatively little about the hardness of MCSP unconditionally. Indeed, until very recently it was unknown whether MCSP can be computed in AC^0[2] (Golovnev et al., ICALP 2019). Our main contribution in this paper is to formulate a new "oracle" variant of circuit complexity and prove that this problem is NP-complete under randomized reductions. In more detail, we define the Minimum Oracle Circuit Size Problem (MOCSP) that takes as input the truth table of a Boolean function f, a size threshold s, and the truth table of an oracle Boolean function O, and determines whether there is a circuit with O-oracle gates and at most s wires that computes f. We prove that MOCSP is NP-complete under randomized polynomial-time reductions. We also extend the recent AC^0[p] lower bound against MCSP by Golovnev et al. to a lower bound against the circuit minimization problem for depth-d formulas, (AC^0_d)-MCSP. We view this result as primarily a technical contribution. In particular, our proof takes a radically different approach from prior MCSP-related hardness results

Crystallization kinetics and role of stress in Al induced layer exchange crystallization process of amorphous SiGe thin film on glass

The present study reports Al induced crystallization (AIC) of amorphous (a)-SiGe in Al-Ge-Si ternary system at low temperature ~ 350 degree C. In addition to crystallization, the isothermal annealing of a-SiGe/AlOx/Al/corning-glass (CG) structure was found to be accompanied by an Al induced layer exchange (ALILE) phenomenon. The evolution of residual stress in the Al layer during isothermal annealing is evaluated using X-ray diffraction based technique to ascertain the role of stress in the ALILE process. A corroboration of the stress with the growth kinetics, analyzed using Avrami theory of phase transformation gives a comprehensive understanding of the ALILE crystallization process in this system. The grown polycrystalline SiGe thin film is a potential candidate for novel technological applications in semiconductor devices.Comment: 24 pages, 11 figure

“Liting it up”: Popular Culture, Indo-Pak Basketball, and South Asian American Institutions

South Asian American participants of a co-ethnic basketball league, known as Indo-Pak Basketball, utilized urban basketball vernacular through the phrase “liting it up” to identify individuals scoring points in great numbers. The person “liting it up” becomes visible and receives recognition. Accordingly, I want to “lite up” the scholarship on South Asian America whereby situating South Asian American religious sites and cultural centers as key arenas for “Americanization” through US popular culture. I situate sport as a key element of popular culture through which South Asian American communities work out, struggle through, and contest notions of self. Informed by an Anthropology of Sport, ethnography of South Asian American communities in Atlanta takes place alongside an examination of the North American Indo-Pak Basketball circuit. Accordingly, my findings indicate that such community formation has also taken shape at the intersections of institutions, gender, and sexuality whereby excluding queers, women, and other communities of color

NP-hardness of circuit minimization for multi-output functions

Can we design efficient algorithms for finding fast algorithms? This question is captured by various circuit minimization problems, and algorithms for the corresponding tasks have significant practical applications. Following the work of Cook and Levin in the early 1970s, a central question is whether minimizing the circuit size of an explicitly given function is NP-complete. While this is known to hold in restricted models such as DNFs, making progress with respect to more expressive classes of circuits has been elusive. In this work, we establish the first NP-hardness result for circuit minimization of total functions in the setting of general (unrestricted) Boolean circuits. More precisely, we show that computing the minimum circuit size of a given multi-output Boolean function f : {0,1}^n ? {0,1}^m is NP-hard under many-one polynomial-time randomized reductions. Our argument builds on a simpler NP-hardness proof for the circuit minimization problem for (single-output) Boolean functions under an extended set of generators. Complementing these results, we investigate the computational hardness of minimizing communication. We establish that several variants of this problem are NP-hard under deterministic reductions. In particular, unless ? = ??, no polynomial-time computable function can approximate the deterministic two-party communication complexity of a partial Boolean function up to a polynomial. This has consequences for the class of structural results that one might hope to show about the communication complexity of partial functions

Pedestrian Flow Characteristics for Different Pedestrian Facilities and Situations

The pedestrian walking data collected at nineteen locations in five cities of India are analyzed in this paper. Pedestrian facilities are classified based on their width as sidewalk, wide-sidewalk and precincts. The analysis indicates that the pedestrian free flow speed is high on sidewalks (1.576 m/s) and low on precincts (1.340 m/s). The increase in width of the facility resulted in increased space available to a pedestrian, but reduced maximum flow rate and optimum density. It is found that the relationship between speed and density follows Underwood (exponential) model on sidewalk of varying widths and Greenshield’s (linear) model on a non-exclusive facility. Bi-directional flow on a facility affects the free flow speed and space available to the pedestrian adversely at high density. Squeezing effect at the centre and follow the predecessor near sides is observed under heavy bidirectional flow. The presence of a bottleneck reduces the free flow speed and maximum flow substantially. Pedestrians moved in layers at high density. Maximum flow rate is observed to be higher on the carriageway (2.067 ped/s) as compared to an exclusive pedestrian facility (1.493 ped/s)