4,594 research outputs found

    Consistency of circuit lower bounds with bounded theories

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    Proving that there are problems in PNP\mathsf{P}^\mathsf{NP} that require boolean circuits of super-linear size is a major frontier in complexity theory. While such lower bounds are known for larger complexity classes, existing results only show that the corresponding problems are hard on infinitely many input lengths. For instance, proving almost-everywhere circuit lower bounds is open even for problems in MAEXP\mathsf{MAEXP}. Giving the notorious difficulty of proving lower bounds that hold for all large input lengths, we ask the following question: Can we show that a large set of techniques cannot prove that NP\mathsf{NP} is easy infinitely often? Motivated by this and related questions about the interaction between mathematical proofs and computations, we investigate circuit complexity from the perspective of logic. Among other results, we prove that for any parameter k≥1k \geq 1 it is consistent with theory TT that computational class C⊈i.o.SIZE(nk){\mathcal C} \not \subseteq \textit{i.o.}\mathrm{SIZE}(n^k), where (T,C)(T, \mathcal{C}) is one of the pairs: T=T21T = \mathsf{T}^1_2 and C=PNP{\mathcal C} = \mathsf{P}^\mathsf{NP}, T=S21T = \mathsf{S}^1_2 and C=NP{\mathcal C} = \mathsf{NP}, T=PVT = \mathsf{PV} and C=P{\mathcal C} = \mathsf{P}. In other words, these theories cannot establish infinitely often circuit upper bounds for the corresponding problems. This is of interest because the weaker theory PV\mathsf{PV} already formalizes sophisticated arguments, such as a proof of the PCP Theorem. These consistency statements are unconditional and improve on earlier theorems of [KO17] and [BM18] on the consistency of lower bounds with PV\mathsf{PV}

    Iterated reflection principles over full disquotational truth

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    Iterated reflection principles have been employed extensively to unfold epistemic commitments that are incurred by accepting a mathematical theory. Recently this has been applied to theories of truth. The idea is to start with a collection of Tarski-biconditionals and arrive by finitely iterated reflection at strong compositional truth theories. In the context of classical logic it is incoherent to adopt an initial truth theory in which A and 'A is true' are inter-derivable. In this article we show how in the context of a weaker logic, which we call Basic De Morgan Logic, we can coherently start with such a fully disquotational truth theory and arrive at a strong compositional truth theory by applying a natural uniform reflection principle a finite number of times

    A study of English-Chinese Simultaneous Interpreting in Conference on Women Rights Under Chernov’s Compression Theory

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    Simultaneous interpreting (SI) means the conveying of information of speakers by interpreters fluently and simultaneously with no long pauses. According to Gile’s theory (1995), interpreters have to possess three abilities, including listening and analysis, production and memory. Given the extreme situation of SI, interpreters must have a nice command of processing strategies to ensure a good delivery. And one of the most important strategies is compression proposed by Chernov (2004). To Chernov’s mind, compression is divided into syllabic compression, lexical compression, semantic compression, syntactic compression and situational compression. The paper mainly discusses the application of compression strategy in E-C discourse under different circumstances
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