719 research outputs found
Feedback Regulation and its Efficiency in Biochemical Networks
Intracellular biochemical networks fluctuate dynamically due to various
internal and external sources of fluctuation. Dissecting the fluctuation into
biologically relevant components is important for understanding how a cell
controls and harnesses noise and how information is transferred over apparently
noisy intracellular networks. While substantial theoretical and experimental
advancement on the decomposition of fluctuation was achieved for feedforward
networks without any loop, we still lack a theoretical basis that can
consistently extend such advancement to feedback networks. The main obstacle
that hampers is the circulative propagation of fluctuation by feedback loops.
In order to define the relevant quantity for the impact of feedback loops for
fluctuation, disentanglement of the causally interlocked influence between the
components is required. In addition, we also lack an approach that enables us
to infer non-perturbatively the influence of the feedback to fluctuation as the
dual reporter system does in the feedforward network. In this work, we resolve
these problems by extending the work on the fluctuation decomposition and the
dual reporter system. For a single-loop feedback network with two components,
we define feedback loop gain as the feedback efficiency that is consistent with
the fluctuation decomposition for feedforward networks. Then, we clarify the
relation of the feedback efficiency with the fluctuation propagation in an
open-looped FF network. Finally, by extending the dual reporter system, we
propose a conjugate feedback and feedforward system for estimating the feedback
efficiency only from the statistics of the system non-perturbatively
Almost Every Simply Typed Lambda-Term Has a Long Beta-Reduction Sequence
It is well known that the length of a beta-reduction sequence of a simply
typed lambda-term of order k can be huge; it is as large as k-fold exponential
in the size of the lambda-term in the worst case. We consider the following
relevant question about quantitative properties, instead of the worst case: how
many simply typed lambda-terms have very long reduction sequences? We provide a
partial answer to this question, by showing that asymptotically almost every
simply typed lambda-term of order k has a reduction sequence as long as
(k-1)-fold exponential in the term size, under the assumption that the arity of
functions and the number of variables that may occur in every subterm are
bounded above by a constant. To prove it, we have extended the infinite monkey
theorem for strings to a parametrized one for regular tree languages, which may
be of independent interest. The work has been motivated by quantitative
analysis of the complexity of higher-order model checking
On Word and Frontier Languages of Unsafe Higher-Order Grammars
Higher-order grammars are an extension of regular and context-free grammars, where nonterminals may take parameters. They have been extensively studied in 1980\u27s, and restudied recently in the context of model checking and program verification. We show that the class of unsafe order-(n+1) word languages coincides with the class of frontier languages of unsafe order-n tree languages. We use intersection types for transforming an order-(n+1) word grammar to a corresponding order-n tree grammar. The result has been proved for safe languages by Damm in 1982, but it has been open for unsafe languages, to our knowledge. Various known results on higher-order grammars can be obtained as almost immediate corollaries of our result
Pumping Lemma for Higher-order Languages
We study a pumping lemma for the word/tree languages generated by higher-order grammars. Pumping lemmas are known up to order-2 word languages (i.e., for regular/context-free/indexed languages), and have been used to show that a given language does not belong to the classes of regular/context-free/indexed languages. We prove a pumping lemma for word/tree languages of arbitrary orders, modulo a conjecture that a higher-order version of Kruskal\u27s tree theorem holds. We also show that the conjecture indeed holds for the order-2 case, which yields a pumping lemma for order-2 tree languages and order-3 word languages
Lambda-Definable Order-3 Tree Functions are Well-Quasi-Ordered
Asada and Kobayashi [ICALP 2017] conjectured a higher-order version of Kruskal\u27s tree theorem, and proved a pumping lemma for higher-order languages modulo the conjecture. The conjecture has been proved up to order-2, which implies that Asada and Kobayashi\u27s pumping lemma holds for order-2 tree languages, but remains open for order-3 or higher. In this paper, we prove a variation of the conjecture for order-3. This is sufficient for proving that a variation of the pumping lemma holds for order-3 tree languages (equivalently, for order-4 word languages)
Size-Preserving Translations from Order-(n+1) Word Grammars to Order-n Tree Grammars
Higher-order grammars have recently been studied actively in the context of automated verification of higher-order programs. Asada and Kobayashi have previously shown that, for any order-(n+1) word grammar, there exists an order-n grammar whose frontier language coincides with the language generated by the word grammar. Their translation, however, blows up the size of the grammar, which inhibited complexity-preserving reductions from decision problems on word grammars to those on tree grammars. In this paper, we present a new translation from order-(n+1) word grammars to order-n tree grammars that is size-preserving in the sense that the size of the output tree grammar is polynomial in the size of an input tree grammar. The new translation and its correctness proof are arguably much simpler than the previous translation and proof
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