Related papers: Instruction sequence size complexity of parity
Transient algebra is a multi-valued algebra for hazard detection in gate circuits. Sequences of alternating 0's and 1's, called transients, represent signal values, and gates are modeled by extensions of boolean functions to transients.…
In his breakthrough paper, Raz showed that any parity learning algorithm requires either quadratic memory or an exponential number of samples [FOCS'16, JACM'19]. A line of work that followed extended this result to a large class of learning…
A boolean expression is in read-once form if each of its variables appears exactly once. When the variables denote independent events in a probability space, the probability of the event denoted by the whole expression in read-once form can…
We study the query complexity of Bayesian Private Learning: a learner wishes to locate a random target within an interval by submitting queries, in the presence of an adversary who observes all of her queries but not the responses. How many…
This paper introduces a combinatorial optimization approach to register allocation and instruction scheduling, two central compiler problems. Combinatorial optimization has the potential to solve these problems optimally and to exploit…
We study the circuit complexity of boolean functions in a certain infinite basis. The basis consists of all functions that take value $1$ on antichains over the boolean cube. We prove that the circuit complexity of the parity function and…
This paper describes a fundamental correspondence between Boolean functions and projection operators in Hilbert space. The correspondence is widely applicable, and it is used in this paper to provide a common mathematical framework for the…
This paper describes a purely functional library for computing level-$p$-complexity of Boolean functions, and applies it to two-level iterated majority. Boolean functions are simply functions from $n$ bits to one bit, and they can describe…
An algorithm for computing the nonlinearity of a Boolean function from its algebraic normal form (ANF) is proposed. By generalizing the expression of the weight of a Boolean function in terms of its ANF coefficients, a formulation of the…
Property Specification Patterns (PSPs) have been proposed to solve recurring specification needs, to ease the formalization of requirements, and enable automated verification thereof. In this paper, we extend PSPs by considering Boolean as…
Boolean functions and binary sequences are main tools used in cryptography. In this work, we introduce a new bijection between the set of Boolean functions and the set of binary sequences with period a power of two. We establish a…
Carefully engineered system prompts play a critical role in guiding the behavior of LLM agents, but their considerable length introduces significant drawbacks, including increased inference latency, higher computational cost, and reduced…
Learning auxiliary tasks, such as multiple predictions about the world, can provide many benefits to reinforcement learning systems. A variety of off-policy learning algorithms have been developed to learn such predictions, but as yet there…
We establish a lower bound for deciding the satisfiability of the conjunction of any two Boolean formulas from a set called a full representation of Boolean functions of $n$ variables - a set containing a Boolean formula to represent each…
Researchers working on the automatic parallelization of programs have long known that too much parallelism can be even worse for performance than too little, because spawning a task to be run on another CPU incurs overheads.…
Learning functional programming requires learning a substitution-based computational model. While substitution should be a familiar concept from high-school algebra, students often have difficulty applying it to new settings, such as…
Memory refinements are designed below to detect those sequences of actions that have been repeated a given number n. Subsequently such sequences are permitted to run without CPU involvement. This mimics human learning. Actions are rehearsed…
Elementary function calls are a common feature in numerical programs. While their implementions in library functions are highly optimized, their computation is nonetheless very expensive compared to plain arithmetic. Full accuracy is,…
Balancing model complexity against the information contained in observed data is the central challenge to learning. In order for complexity-efficient models to exist and be discoverable in high dimensions, we require a computational…
A combination of program algebra with the theory of meadows is designed leading to a theory of computation in algebraic structures which use in addition to a zero test and copying instructions the instruction set $\{x \Leftarrow 0, x…