We investigate questions related to the time evolution of discrete graph
dynamical systems where each node has a state from {0,1}. The configuration of
a system at any time instant is a Boolean vector that specifies the state of each
node at that instant. We say that two configurations are similar if the Hamming
distance between them is small. Also, a predecessor of a configuration B is a
configuration A such that B can be reached in one step from A. We study problems
related to the similarity of predecessor configurations from which two similar
configurations can be reached in one time step. We address these problems
both analytically and experimentally. Our analytical results point out that the
level of similarity between predecessors of two similar configurations depends
on the local functions of the dynamical system. Our experimental results, which
consider random graphs as well as small world networks, rely on the fact that
the problem of finding predecessors can be reduced to the Boolean Satisfiability
problem (SAT).
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Testing phase space properties of synchronous dynamical systems with nested canalyzing local functions.
Discrete graphical dynamical systems serve as effective formal models in many contexts, including simulations of agent-based models, propagation of contagions in social networks and study of biological phenomena. A class of Boolean functions, called nested canalyzing functions (NCFs), has been used as a good model of certain biological phenomena. Motivated by these biological applications, we study a variety of analysis problems for synchronous graphical dynamical systems (SyDSs) over the Boolean domain, where each local function is an NCF. Each analysis problem involves testing whether the phase space of a given SyDS satisfies a certain property. We present intractability results for some properties as well as efficient algorithms for others. In several cases, our results clearly delineate intractable and efficiently solvable versions of problems
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- Award ID(s):
- 1633028
- NSF-PAR ID:
- 10067760
- Date Published:
- Journal Name:
- AAMAS 2018
- Page Range / eLocation ID:
- 1585-1594
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
