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This thesis details a project to define a fully compositional theory of synchronous sequential circuits built from primitive components, motivated by applying techniques successfully used in programming languages to hardware. The first part…
Let $ACC \circ THR$ be the class of constant-depth circuits comprised of AND, OR, and MOD$m$ gates (for some constant $m > 1$), with a bottom layer of gates computing arbitrary linear threshold functions. This class of circuits can be seen…
Probabilistic circuits (PCs) are a unifying representation for probabilistic models that support tractable inference. Numerous applications of PCs like controllable text generation depend on the ability to efficiently multiply two circuits.…
Generalized counting constraint satisfaction problems include Holant problems with planarity restrictions; polynomial-time algorithms for such problems include matchgates and matchcircuits, which are based on Pfaffians. In particular, they…
Probabilistic circuits (PCs) offer a promising avenue to perform embedded reasoning under uncertainty. They support efficient and exact computation of various probabilistic inference tasks by design. Hence, hardware-efficient computation of…
Using a proofs-as-programs correspondence, Terui was able to compare two models of parallel computation: Boolean circuits and proof nets for multiplicative linear logic. Mogbil et. al. gave a logspace translation allowing us to compare…
In this paper, we present a robust adaptive model predictive control (MPC) scheme for linear systems subject to parametric uncertainty and additive disturbances. The proposed approach provides a computationally efficient formulation with…
Let $1 \le s < t$, $N \ge 1$ be integers and a complex electronic circuit of size $t$ is said to be an $s$-active, $\; s \ll t$, and can work as a system block if not more than $s$ elements of the circuit are defective. Otherwise, the…
We study the representation of systems S of linear equations over the two-element field (aka xor- or parity-constraints) via conjunctive normal forms F (boolean clause-sets). First we consider the problem of finding an "arc-consistent"…
Linear active-power-only DC power flow approximations are pervasive in the planning and control of power systems. However, these approximations fail to capture reactive power and voltage magnitudes, both of which are necessary in many…
In stochastic computing (SC), a real-valued number is represented by a stochastic bit stream, encoding its value in the probability of obtaining a one. This leads to a significantly lower hardware effort for various functions and provides a…
We study uniformity conditions for parameterized Boolean circuit families. Uniformity conditions require that the infinitely many circuits in a circuit family are in some sense easy to construct from one shared description. For shallow…
What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…
Polynomial optimization encompasses a broad class of problems in which both the objective function and constraints are polynomial functions of the decision variables. In recent years, a substantial body of research has focused on…
Dynamic logic is a modal logic for reasoning about programs. A cyclic proof system is a proof system that allows proofs containing cycles and is an alternative to a proof system containing (co-)induction. This paper introduces a sequent…
Probabilistic sentential decision diagrams are a class of structured-decomposable probabilistic circuits especially designed to embed logical constraints. To adapt the classical LearnSPN scheme to learn the structure of these models, we…
Approximate Bayesian Computation (ABC) is a powerful method for carrying out Bayesian inference when the likelihood is computationally intractable. However, a drawback of ABC is that it is an approximate method that induces a systematic…
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…
We study atom canonicity for several varieties of cylindric like algebras that contain properly the variety of representable algebras. The algebras in such varieties have relativized representations, and we thereby obtain many omitting…
Answer-set programming (ASP) has emerged recently as a viable programming paradigm well attuned to search problems in AI, constraint satisfaction and combinatorics. Propositional logic is, arguably, the simplest ASP system with an intuitive…