65 research outputs found
Computational Complexity of Minimal Trap Spaces in Boolean Networks
Trap spaces of a Boolean network (BN) are the sub-hypercubes closed by the
function of the BN. A trap space is minimal if it does not contain any smaller
trap space. Minimal trap spaces have applications for the analysis of dynamic
attractors of BNs with various update modes. This paper establishes
computational complexity results of three decision problems related to minimal
trap spaces of BNs: the decision of the trap space property of a sub-hypercube,
the decision of its minimality, and the decision of the belonging of a given
configuration to a minimal trap space. Under several cases on Boolean function
specifications, we investigate the computational complexity of each problem. In
the general case, we demonstrate that the trap space property is coNP-complete,
and the minimality and the belonging properties are -complete.
The complexities drop by one level in the polynomial hierarchy whenever the
local functions of the BN are either unate, or are specified using truth-table,
binary decision diagrams, or double-DNF (Petri net encoding): the trap space
property can be decided in P, whereas the minimality and the belonging are
coNP-complete. When the BN is given as its functional graph, all these problems
can be decided by deterministic polynomial time algorithms
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