Congeneric Intervals Chain

A Congeneric intervals chain is an Partial Interval Chain where all non-empty elements are part of the one trace path (trace to the same terminal value).

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Mathematical Definition

Let \(-\) is empty value

Let \(IC_p\) is Partial interval chain \(IC_p : \{1, ..., l\} \longrightarrow \{1,...,l\} \cup \{-\},\)

Let \(Trace_p\) is trace function of partial interval chain

\[Trace_p : \big\{Binding_p\big\} \times \big\{ IC_p \big\} \longrightarrow \big\{ R_p \big\},\]

\(IC_p\) is called \(IC_c\) Congeneric interval chain if

\[trace = Trace_p(b_p, IC_P)\]

\[trace(i) = trace(j) \bigg| \forall i \ne j, IC_{p}(i) \notin \{-\} \land IC_{p}(j) \notin \{-\}\]