74,477 research outputs found
Approximating Optimal Bounds in Prompt-LTL Realizability in Doubly-exponential Time
We consider the optimization variant of the realizability problem for Prompt
Linear Temporal Logic, an extension of Linear Temporal Logic (LTL) by the
prompt eventually operator whose scope is bounded by some parameter. In the
realizability optimization problem, one is interested in computing the minimal
such bound that allows to realize a given specification. It is known that this
problem is solvable in triply-exponential time, but not whether it can be done
in doubly-exponential time, i.e., whether it is just as hard as solving LTL
realizability.
We take a step towards resolving this problem by showing that the optimum can
be approximated within a factor of two in doubly-exponential time. Also, we
report on a proof-of-concept implementation of the algorithm based on bounded
LTL synthesis, which computes the smallest implementation of a given
specification. In our experiments, we observe a tradeoff between the size of
the implementation and the bound it realizes. We investigate this tradeoff in
the general case and prove upper bounds, which reduce the search space for the
algorithm, and matching lower bounds.Comment: In Proceedings GandALF 2016, arXiv:1609.0364
Protein logic: a statistical mechanical study of signal integration at the single-molecule level
Information processing and decision making is based upon logic operations,
which in cellular networks has been well characterized at the level of
transcription. In recent years however, both experimentalists and theorists
have begun to appreciate that cellular decision making can also be performed at
the level of a single protein, giving rise to the notion of protein logic. Here
we systematically explore protein logic using a well known statistical
mechanical model. As an example system, we focus on receptors which bind either
one or two ligands, and their associated dimers. Notably, we find that a single
heterodimer can realize any of the 16 possible logic gates, including the XOR
gate, by variation of biochemical parameters. We then introduce the novel idea
that a set of receptors with fixed parameters can encode functionally unique
logic gates simply by forming different dimeric combinations. An exhaustive
search reveals that the simplest set of receptors (two single-ligand receptors
and one double-ligand receptor) can realize several different groups of three
unique gates, a result for which the parametric analysis of single receptors
and dimers provides a clear interpretation. Both results underscore the
surprising functional freedom readily available to cells at the single-protein
level.Comment: 19 pages, 4 figures and 9 pages S
- …