Problems and Exercises in Discrete Mathematics
Many years of practical experience in teaching discrete mathematics form the basis of this text book. Part I contains problems on such topics as Boolean algebra, k-valued logics, graphs and networks, elements of coding theory, automata theory, algorithms theory, combinatorics, Boolean minimization and logical design. The exercises are preceded by ample theoretical background material. For further study the reader is referred to the extensive bibliography. Part II follows the same structure as Part I, and gives helpful hints and solutions.
Audience:This book will be of great value to undergraduate students of discrete mathematics, whereas the more difficult exercises, which comprise about one-third of the material, will also appeal to postgraduates and researchers.
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Closed Classes and Completeness in Boolean Algebra
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alphabet an+2 arbitrary assume binary Boolean function called canonical equations chain closed class code words coefficients columns complete in Pk connected graph construct contact circuit contains corresponding cube Bn cycles d.-function defined denoted digraph elements equal equivalent Example exists f(in Figure Find the number formula function f(xn graph G Hamiltonian cycle Hence Hint induction inequality input integer irredundant Ji(x jo(x length linear linear code linearly independent matrix max(x min(x minimal monotone monotone function Moore diagram number of pairwise number of vertices obtain operator output pairs pairwise different permutation poles polynomial prefix prefix code primitive recursive primitive recursive functions Problem Prove pseudograph qi(t realizing recurrence relation recursive functions reduced d.n.f. represented rooted tree rows satisfies self-dual sequence Solution subgraph subset superposition symbol tuple Turing machine valid value vector variables Xi vector vertex weight xix2 zero