Tipo
Artigos em Conferência
Tipo de Documento
Artigo Completo
Título
Lifting to Parity Decision Trees via Stifling
Participantes na publicação
Arkadev Chattopadhyay (Author)
Nikhil S Mande (Author)
Swagato Sanyal (Author)
Suhail Sherif (Author)
Dep. Matemática
Resumo
We show that the deterministic decision tree complexity of a (partial) function or relation f lifts to the deterministic parity decision tree (PDT) size complexity of the composed function/relation 'f composed with g' as long as the gadget g satisfies a property that we call stifling. We observe that several simple gadgets of constant size, like Indexing on 3 input bits, Inner Product on 4 input bits, Majority on 3 input bits and random functions, satisfy this property. It can be shown that existing randomized communication lifting theorems ([Göös, Pitassi, Watson. SICOMP'20], [Chattopadhyay et al. SICOMP'21]) imply PDT-size lifting. However there are two shortcomings of this approach: first they lift randomized decision tree complexity of f, which could be exponentially smaller than its deterministic counterpart when either f is a partial function or even a total search problem. Second, the size of the gadgets in such lifting theorems are as large as logarithmic in the size of the input to f. Reducing the gadget size to a constant is an important open problem at the frontier of current research. Our result shows that even a random constant-size gadget does enable lifting to PDT size. Further, it also yields the first systematic way of turning lower bounds on the width of tree-like resolution proofs of the unsatisfiability of constant-width CNF formulas to lower bounds on the size of tree-like proofs in the resolution with parity system of the unsatisfiability of closely related constant-width CNF formulas.
Editor
Yael Tauman Kalai
Data de Submissão/Pedido
2022-09-8
Data de Aceitação
2022-10-30
Data de Publicação
2023-02-01
Evento
14th Innovations in Theoretical Computer Science Conference (ITCS 2023)
Identificadores da Publicação
ISBN - 9783959772631
Editora
Schloss-Dagstuhl - Leibniz Zentrum für Informatik
Número de Páginas
20
Página Inicial
33:1
Página Final
33:20
Identificadores do Documento
DOI -
https://doi.org/10.4230/LIPIcs.ITCS.2023.33
Identificadores de Qualidade
CORE A (2023) - Theory of computation
Keywords
parity decision trees
proof complexity
lifting theorems
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