<table><thead><tr><th>Notation</th><th>Meaning</th><th>Where Defined</th></tr></thead><tbody><tr><td>pt(π)</td><td>participant of action π</td><td>before Def. 2.1</td></tr><tr><td>part(σ)</td><td>participants of trace σ</td><td>Def. 2.3</td></tr><tr><td>D(S)</td><td>domain of configurations of ES S</td><td>Def. 3.5</td></tr><tr><td>act(η)</td><td>action of p-event η</td><td>after Def. 4.1</td></tr><tr><td>S<sup>P</sup>(P)</td><td>event structure of process P</td><td>Def. 4.3</td></tr><tr><td>PE(P)</td><td>set of p-events of S<sup>P</sup>(P)</td><td>Def. 4.3</td></tr><tr><td>p :: η</td><td>located event, p-event η located at participant p</td><td>Def. 5.1</td></tr><tr><td>η<sup>P</sup>p</td><td>projection of p-event η on participant p</td><td>Def. 5.2</td></tr><tr><td>Θ ⋈ Θ'</td><td>duality of undirected action sequences Θ and Θ'</td><td>Def. 5.3</td></tr><tr><td>p :: η ⋈ q :: η'</td><td>duality of located events p :: η and q :: η'</td><td>Def. 5.4</td></tr><tr><td>cm(v)</td><td>communication of n-event v</td><td>after Def. 5.5</td></tr><tr><td>loc(v)</td><td>set of locations of n-event v</td><td>after Def. 5.5</td></tr><tr><td>p :: η ∈ E</td><td>occurrence of located event p :: η in some n-event of E</td><td>Def. 5.6</td></tr><tr><td>n(E)</td><td>narrowing of the n-event set E</td><td>Def. 5.11</td></tr><tr><td>S<sup>N</sup>(N)</td><td>event structure of network N</td><td>Def. 5.13</td></tr><tr><td>CE(N)</td><td>set of candidate n-events of S<sup>N</sup>(N)</td><td>Def. 5.13</td></tr><tr><td>N<sup>E</sup>(N)</td><td>set of n-events of S<sup>N</sup>(N)</td><td>Def. 5.13</td></tr><tr><td>ϑ ↘ n</td><td>prefix of length n of ϑ</td><td>before Prop. 5.22</td></tr><tr><td>proj<sub>p</sub>(v)</td><td>projection of n-event v on participant p</td><td>Def. 5.25</td></tr><tr><td>part(G)</td><td>participants of global type G</td><td>after Def. 6.1</td></tr><tr><td>G ⊠ p</td><td>projection of global type G on participant p</td><td>Figure 2</td></tr><tr><td>σ[i]</td><td>i-th element of trace σ</td><td>before Def. 7.1</td></tr><tr><td>σ[i ... j]</td><td>subtrace σ[i] ... σ[j] of trace σ</td><td>before Def. 7.1</td></tr><tr><td>σ ~ σ'</td><td>permutation equivalence of traces</td><td>Def. 7.1</td></tr><tr><td>[σ]<sub>~</sub></td><td>equivalence class of trace σ w.r.t ~</td><td>Def. 7.1</td></tr><tr><td>last(σ)</td><td>last communication of trace σ</td><td>before Lemma 7.4</td></tr><tr><td>cm(γ)</td><td>communication of g-event γ</td><td>Def. 7.5</td></tr><tr><td>σ ◦ γ</td><td>retrieval of g-event γ before trace σ</td><td>Def. 7.6(1) and (2)</td></tr><tr><td>ev(σ)</td><td>g-event generated by trace σ</td><td>Def. 7.7</td></tr><tr><td>σ@p</td><td>projection of trace σ on participant p</td><td>Def. 7.9(1) and (2)</td></tr><tr><td>S<sup>G</sup>(G)</td><td>event structure of global type G</td><td>Def. 7.11</td></tr><tr><td>G<sup>E</sup>(G)</td><td>set of g-events of S<sup>G</sup>(G)</td><td>Def. 7.11</td></tr><tr><td>σ ◊ v</td><td>retrieval of n-event v before trace σ</td><td>Def. 8.1(1) and (3)</td></tr><tr><td>σ ◊ v</td><td>residual of n-event v after trace σ</td><td>Def. 8.1(2) and (3)</td></tr><tr><td>nec(σ)</td><td>sequence of n-events corresponding to trace σ</td><td>Def. 8.3</td></tr><tr><td>σ • γ</td><td>residual of g-event γ after trace σ</td><td>Def. 8.9(1) and (2)</td></tr><tr><td>gec(σ)</td><td>sequence of g-events corresponding to trace σ</td><td>Def. 8.13</td></tr></tbody></table>