69,649 research outputs found
Minimal Proof Search for Modal Logic K Model Checking
Most modal logics such as S5, LTL, or ATL are extensions of Modal Logic K.
While the model checking problems for LTL and to a lesser extent ATL have been
very active research areas for the past decades, the model checking problem for
the more basic Multi-agent Modal Logic K (MMLK) has important applications as a
formal framework for perfect information multi-player games on its own.
We present Minimal Proof Search (MPS), an effort number based algorithm
solving the model checking problem for MMLK. We prove two important properties
for MPS beyond its correctness. The (dis)proof exhibited by MPS is of minimal
cost for a general definition of cost, and MPS is an optimal algorithm for
finding (dis)proofs of minimal cost. Optimality means that any comparable
algorithm either needs to explore a bigger or equal state space than MPS, or is
not guaranteed to find a (dis)proof of minimal cost on every input.
As such, our work relates to A* and AO* in heuristic search, to Proof Number
Search and DFPN+ in two-player games, and to counterexample minimization in
software model checking.Comment: Extended version of the JELIA 2012 paper with the same titl
Coupled Reversible and Irreversible Bistable Switches Underlying TGF-\beta-induced Epithelial to Mesenchymal Transition
Epithelial to mesenchymal transition (EMT) plays important roles in embryonic
development, tissue regeneration and cancer metastasis. While several feedback
loops have been shown to regulate EMT, it remains elusive how they coordinately
modulate EMT response to TGF-\beta treatment. We construct a mathematical model
for the core regulatory network controlling TGF-\beta-induced EMT. Through
deterministic analyses and stochastic simulations, we show that EMT is a
sequential two-step program that an epithelial cell first transits to partial
EMT then to the mesenchymal state, depending on the strength and duration of
TGF-\beta stimulation. Mechanistically the system is governed by coupled
reversible and irreversible bistable switches. The SNAIL1/miR-34 double
negative feedback loop is responsible for the reversible switch and regulates
the initiation of EMT, while the ZEB/miR-200 feedback loop is accountable for
the irreversible switch and controls the establishment of the mesenchymal
state. Furthermore, an autocrine TGF-\beta/miR-200 feedback loop makes the
second switch irreversible, modulating the maintenance of EMT. Such coupled
bistable switches are robust to parameter variation and molecular noise. We
provide a mechanistic explanation on multiple experimental observations. The
model makes several explicit predictions on hysteretic dynamic behaviors,
system response to pulsed stimulation and various perturbations, which can be
straightforwardly tested.Comment: 32 pages, 8 figures, accepted by Biophysical Journa
Propagators and Solvers for the Algebra of Modular Systems
To appear in the proceedings of LPAR 21.
Solving complex problems can involve non-trivial combinations of distinct
knowledge bases and problem solvers. The Algebra of Modular Systems is a
knowledge representation framework that provides a method for formally
specifying such systems in purely semantic terms. Formally, an expression of
the algebra defines a class of structures. Many expressive formalism used in
practice solve the model expansion task, where a structure is given on the
input and an expansion of this structure in the defined class of structures is
searched (this practice overcomes the common undecidability problem for
expressive logics). In this paper, we construct a solver for the model
expansion task for a complex modular systems from an expression in the algebra
and black-box propagators or solvers for the primitive modules. To this end, we
define a general notion of propagators equipped with an explanation mechanism,
an extension of the alge- bra to propagators, and a lazy conflict-driven
learning algorithm. The result is a framework for seamlessly combining solving
technology from different domains to produce a solver for a combined system.Comment: To appear in the proceedings of LPAR 2
Ackermannian and Primitive-Recursive Bounds with Dickson's Lemma
Dickson's Lemma is a simple yet powerful tool widely used in termination
proofs, especially when dealing with counters or related data structures.
However, most computer scientists do not know how to derive complexity upper
bounds from such termination proofs, and the existing literature is not very
helpful in these matters.
We propose a new analysis of the length of bad sequences over (N^k,\leq) and
explain how one may derive complexity upper bounds from termination proofs. Our
upper bounds improve earlier results and are essentially tight
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