An extensive English language bibliography on graph theory and its applications, supplement 1

Graph theory and its applications - bibliography, supplement

An extensive English language bibliography on graph theory and its applications

Bibliography on graph theory and its application

A Rubik's Cube inspired approach to Clifford synthesis

The problem of decomposing an arbitrary Clifford element into a sequence of Clifford gates is known as Clifford synthesis. Drawing inspiration from similarities between this and the famous Rubik's Cube problem, we develop a machine learning approach for Clifford synthesis based on learning an approximation to the distance to the identity. This approach is probabilistic and computationally intensive. However, when a decomposition is successfully found, it often involves fewer gates than existing synthesis algorithms. Additionally, our approach is much more flexible than existing algorithms in that arbitrary gate sets, device topologies, and gate fidelities may incorporated, thus allowing for the approach to be tailored to a specific device.Comment: 14 pages, 4 figure

On Continuous Local BDD-Based Search for Hybrid SAT Solving

We explore the potential of continuous local search (CLS) in SAT solving by proposing a novel approach for finding a solution of a hybrid system of Boolean constraints. The algorithm is based on CLS combined with belief propagation on binary decision diagrams (BDDs). Our framework accepts all Boolean constraints that admit compact BDDs, including symmetric Boolean constraints and small-coefficient pseudo-Boolean constraints as interesting families. We propose a novel algorithm for efficiently computing the gradient needed by CLS. We study the capabilities and limitations of our versatile CLS solver, GradSAT, by applying it on many benchmark instances. The experimental results indicate that GradSAT can be a useful addition to the portfolio of existing SAT and MaxSAT solvers for solving Boolean satisfiability and optimization problems.Comment: AAAI 2

Submicron Systems Architecture: Semiannual Technical Report

No abstract available

Submicron Systems Architecture Project: Semiannual Technial Report

No abstract available

Application of Logic Synthesis Toward the Inference and Control of Gene Regulatory Networks

In the quest to understand cell behavior and cure genetic diseases such as cancer, the fundamental approach being taken is undergoing a gradual change. It is becoming more acceptable to view these diseases as an engineering problem, and systems engineering approaches are being deployed to tackle genetic diseases. In this light, we believe that logic synthesis techniques can play a very important role. Several techniques from the field of logic synthesis can be adapted to assist in the arguably huge effort of modeling cell behavior, inferring biological networks, and controlling genetic diseases. Genes interact with other genes in a Gene Regulatory Network (GRN) and can be modeled as a Boolean Network (BN) or equivalently as a Finite State Machine (FSM). As the expression of genes deter- mine cell behavior, important problems include (i) inferring the GRN from observed gene expression data from biological measurements, and (ii) using the inferred GRN to explain how genetic diseases occur and determine the ”best” therapy towards treatment of disease. We report results on the application of logic synthesis techniques that we have developed to address both these problems. In the first technique, we present Boolean Satisfiability (SAT) based approaches to infer the predictor (logical support) of each gene that regulates melanoma, using gene expression data from patients who are suffering from the disease. From the output of such a tool, biologists can construct targeted experiments to understand the logic functions that regulate a particular target gene. Our second technique builds upon the first, in which we use a logic synthesis technique; implemented using SAT, to determine gene regulating functions for predictors and gene expression data. This technique determines a BN (or family of BNs) to describe the GRN and is validated on a synthetic network and the p53 network. The first two techniques assume binary valued gene expression data. In the third technique, we utilize continuous (analog) expression data, and present an algorithm to infer and rank predictors using modified Zhegalkin polynomials. We demonstrate our method to rank predictors for genes in the mutated mammalian and melanoma networks. The final technique assumes that the GRN is known, and uses weighted partial Max-SAT (WPMS) towards cancer therapy. In this technique, the GRN is assumed to be known. Cancer is modeled using a stuck-at fault model, and ATPG techniques are used to characterize genes leading to cancer and select drugs to treat cancer. To steer the GRN state towards a desirable healthy state, the optimal selection of drugs is formulated using WPMS. Our techniques can be used to find a set of drugs with the least side-effects, and is demonstrated in the context of growth factor pathways for colon cancer