Finite State Transducers and System Composition Sample Clauses

Finite State Transducers and System Composition. In the following we consider systems that are composed from sets of so-called transducers, which are finite state ma- chines operating on distinct input and output ports. Transduc- ers are a well-established formalism with Xxxxx- and Xxxxx- machines [14], [15] as their most common representatives. We assume a global non-empty finite set P = {p1, ..., pn} Gj(s) = σ|sP outt ⇐⇒ G(s) = σ. A system is a set = F1, . . . , Fm of FSTs such that for all Fi = (ΣP , Pini, Pouti, Si, si,0, Ti, Gi) and Fj = (ΣP , Pinj, Poutj, Sj, sj,0, Tj, Gj) with i j the relation Pini ∩ Pinj = Pouti ∩ Poutj = ∅ holds. Composition of S S is the FST FS = (ΣP , Pin, Pout, S, s0, T, G) where • Pin = j∈{1,...,m} Pinj \ Pout S • Pout = j∈{1,...,m} Poutj ∈ of ports, and alphabets Σp for all p P . We require a special ∈ ∈ × ×