3 research outputs found
Obtaining combinatorial structures associated with low-dimensional Leibniz algebras
In this paper, we analyze the relation between Leibniz algebras and combinatorial structures. More concretely, we study the properties to be satisfied by (pseudo)digraphs so that they are associated with low-dimensional Leibniz algebras. We present some results related to
this association and show an algorithmic method to obtain them, which has been implemented with Maple
Modular Decomposition of Hierarchical Finite State Machines
In this paper we develop an analogue of the graph-theoretic `modular
decomposition' in automata theory. This decomposition allows us to identify
hierarchical finite state machines (HFSMs) equivalent to a given finite state
machine (FSM). We provide a definition of a module in an FSM, which is a
collection of nodes which can be treated as a nested FSM. We identify a
well-behaved subset of FSM modules called thin modules, and represent these
using a linear-space directed graph we call a decomposition tree. We prove that
every FSM has a unique decomposition tree which uniquely stores each thin
module. We provide an algorithm for finding the decomposition tree of
an -state -alphabet FSM. The decomposition tree allows us to extend FSMs
to equivalent HFSMs. For thin HFSMs, which are those where each nested FSM is a
thin module, we can construct an equivalent maximally-hierarchical HFSM in
polynomial time.Comment: 38 pages, 11 figures. Submitted to Theoretical Computer Scienc