Generalization to d-dimensions of a fermionic path integral for exact enumeration of polygons on hypercubic lattices. [PDF]
Sci RepThe generating function for polygons on the square lattice has been known for many decades and is closely related to the path integral formulation of a free fermion model.
Ostilli M +3 more
europepmc +2 more sources
Revisiting Explicit Enumeration for Exact Synthesis
Euromicro Symposium on Digital Systems Design, 2020 The problem of generating a minimal implementation of a given Boolean function is called exact synthesis. The parameter to be minimized is often the total number of gates used for the implementation.
Goerschwin Fey +2 more
exaly +2 more sources
Exact Bayesian Inference on Discrete Models via Probability Generating Functions: A Probabilistic Programming Approach [PDF]
Neural Information Processing Systems, 2023 We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to many discrete inference problems, even with infinite support and continuous priors.
Fabian Zaiser, A. Murawski, Luke Ong
semanticscholar +1 more source
Generating Functions for Asymmetric Random Walk Processes with Double Absorbing Barriers [PDF]
Social Science Research Network, 2022 Generating functions for asymmetric step-size paths restricted by two absorbing barriers are derived. The method begins by applying the Lagrange inversion formula to arbitrary powers of roots of the characteristic equation, that being a trinomial, which ...
Cetin Hakimoglu-Brown
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Generating functions of non-backtracking walks on weighted digraphs: radius of convergence and Ihara's theorem [PDF]
Linear Algebra and its Applications, 2023 It is known that the generating function associated with the enumeration of non-backtracking walks on finite graphs is a rational matrix-valued function of the parameter; such function is also closely related to graph-theoretical results such as Ihara's ...
V. Noferini, María C. Quintana
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Exact enumeration of satisfiable 2-SAT formulae [PDF]
Combinatorial Theory, 2021 We obtain exact expressions counting the satisfiable 2-SAT formulae and describe the structure of associated implication digraphs. Our approach is based on generating function manipulations.
S. Dovgal +2 more
semanticscholar +1 more source
Heuristic Logic Resynthesis Algorithms at the Core of Peephole Optimization
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2023 Logic resynthesis is one of the core problems in modern peephole logic optimization algorithms. Given a target function and a set of existing functions, logic resynthesis asks for a circuit reusing some of the existing functions and generating the target.
Siang-Yun Lee, G. Micheli
semanticscholar +1 more source
Exact enumeration of graphs and bipartite graphs with degree constraints
European Conference on Combinatorics, Graph Theory and Applications, 2023 We provide a new explicit formula enumerating graphs with constraints on their degrees, such as regular graphs, and extend it to bipartite graphs. It relies on generating function manipulations and Hadamard products.\\ \textbf{Keywords.} regular graphs ...
Emma Caizergues, Élie de Panafieu
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Exact penalty functions with multidimensional penalty parameter and adaptive penalty updates [PDF]
Optimization Letters, 2021 We present a general theory of exact penalty functions with vectorial (multidimensional) penalty parameter for optimization problems in infinite dimensional spaces. In comparison with the scalar case, the use of vectorial penalty parameters provides much
M. Dolgopolik
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An exact solution method for the enumeration of connected Feynman diagrams [PDF]
Journal of Physics A: Mathematical and Theoretical, 2020 We completely generalize previous results related to the counting of connected Feynman diagrams. We use a generating function approach, which encodes the Wick contraction combinatorics of the respective connected diagrams.
E. Castro, I. Roditi
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