Binary number

Summary

A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" (one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation. Negative numbers are commonly represented in binary using two's complement. History The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel y Lobkowitz, and Gottfried Leibniz. However, systems related to binary numbers have appeared earlier in mult

Official source

https://en.wikipedia.org/wiki/Binary_number

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Parity-regular Steinhaus graphs

Maxime Augier

Steinhaus graphs on n vertices are certain simple graphs in bijective correspondence with binary {0,1}-sequences of length n-1. A conjecture of Dymacek in 1979 states that the only nontrivial regular Steinhaus graphs are those corresponding to the periodic binary sequences 110 ... 110 of any length n-1 = 3m. By an exhaustive search the conjecture was known to hold up to 25 vertices. We report here that it remains true up to 117 vertices. This is achieved by considering the weaker notion of parity-regular Steinhaus graphs, where all vertex degrees have the same parity. We show that these graphs can be parametrized by an F-2-vector space of dimension approximately n/3 and thus constitute an efficiently describable domain where true regular Steinhaus graphs can be searched by computer.

American Mathematical Society2008

Decision Rule Bounds for Two-Stage Stochastic Bilevel Programs

Daniel Kuhn

We study stochastic bilevel programs where the leader chooses a binary here-and-now decision and the follower responds with a continuous wait-and-see-decision. Using modern decision rule approximations, we construct lower bounds on an optimistic version and upper bounds on a pessimistic version of the leader's problem. Both bounding problems are equivalent to explicit mixed-integer linear programs that are amenable to efficient numerical solution. The method is illustrated through a facility location problem involving sellers and customers with conflicting preferences.

2018

With the widespread deployment of Control-Flow Integrity (CFI), control-flow hijacking attacks, and consequently code reuse attacks, are significantly more difficult. CFI limits control flow to well-known locations, severely restricting arbitrary code execution. Assessing the remaining attack surface of an application under advanced control-flow hijack defenses such as CFI and shadow stacks remains an open problem. We introduce BOPC, a mechanism to automatically assess whether an attacker can execute arbitrary code on a binary hardened with CFI/shadow stack defenses. BOPC computes exploits for a target program from payload specifications written in a Turing-complete, high-level language called SPL that abstracts away architecture and program-specific details. SPL payloads are compiled into a program trace that executes the desired behavior on top of the target binary. The input for BOPC is an SPL payload, a starting point (e.g., from a fuzzer crash) and an arbitrary memory write primitive that allows application state corruption. To map SPL payloads to a program trace, BOPC introduces Block Oriented Programming (BOP), a new code reuse technique that utilizes entire basic blocks as gadgets along valid execution paths in the program, i.e., without violating CFI or shadow stack policies. We find that the problem of mapping payloads to program traces is NP-hard, so BOPC first reduces the search space by pruning infeasible paths and then uses heuristics to guide the search to probable paths. BOPC encodes the BOP payload as a set of memory writes. We execute 13 SPL payloads applied to 10 popular applications. BOPC successfully finds payloads and complex execution traces which would likely not have been found through manual analysis - while following the target's Control-Flow Graph under an ideal CFI policy in 81% of the cases.

ASSOC COMPUTING MACHINERY2018