{"product_id":"the-graph-isomorphism-problem-its-structural-complexity-progress-in-theoretical-computer-science-9781461267126","title":"The Graph Isomorphism Problem Its Structural Complexity Progress in Theoretical Computer Science","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003ePreliminaries.- 1 Decision Problems, Search Problems, and Counting Problems.- 1.1 NP-Completeness.- 1.2 Reducing the Construction Problem to the Decision Problem.- 1.3 Counting versus Deciding for Graph Isomorphism.- 1.4 Uniqueness of the Solution.- 1.5 Reducing Multiple Questions to One.- 2 Quantifiers, Games, and Interactive Proofs.- 2.1 The Polynomial-Time Hierarchy.- 2.2 Interactive Proof Systems.- 2.3 Probabilistic Classes.- 2.4 Lowness and Collapses.- 3 Circuits and Sparse Sets.- 3.1 Polynomial Size Circuits.- 3.2 Reductions to Sparse Sets.- 4 Counting Properties.- 4.1 Decision Reduces to Parity.- 4.2 Graph Isomorphism is Low for PP.- 4.3 The Reconstruction Conjecture.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreliminaries.- 1 Decision Problems, Search Problems, and Counting Problems.- 1.1 NP-Completeness.- 1.1.1 The Classes P and NP.- 1.1.2 Reducibility.- 1.2 Reducing the Construction Problem to the Decision Problem.- 1.3 Counting versus Deciding for Graph Isomorphism.- 1.4 Uniqueness of the Solution.- 1.4.1 Random Reductions.- 1.4.2 Promise Problems.- 1.5 Reducing Multiple Questions to One.- 2 Quantifiers, Games, and Interactive Proofs.- 2.1 The Polynomial-Time Hierarchy.- 2.2 Interactive Proof Systems.- 2.2.1 The Class IP.- 2.2.2 Zero-Knowledge.- 2.3 Probabilistic Classes.- 2.3.1 Probability Amplification.- 2.3.2 The BP-Operator.- 2.3.3 Arthur-Merlin Games.- 2.4 Lowness and Collapses.- 3 Circuits and Sparse Sets.- 3.1 Polynomial Size Circuits.- 3.1.1 Circuits for NP.- 3.1.2 Circuits for Graph Isomorphism.- 3.2 Reductions to Sparse Sets.- 4 Counting Properties.- 4.1 Decision Reduces to Parity.- 4.2 Graph Isomorphism is Low for PP.- 4.3 The Reconstruction Conjecture.","brand":"Birkhauser Boston","offers":[{"title":"Default Title","offer_id":52151272210775,"sku":"9781461267126","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781461267126.jpg?v=1762960660","url":"https:\/\/bookcurl.com\/products\/the-graph-isomorphism-problem-its-structural-complexity-progress-in-theoretical-computer-science-9781461267126","provider":"Book Curl","version":"1.0","type":"link"}