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Table 2 
Transitions for the top–down and bottom–up generation system. Stack ∑ is represented as a list with its head to the right (with tail σ), same for stack N (with tail β).
 Top–down Transitions
NT(X) ([σ|X′], X, ε, [β|X′], P(X′)) ⇒ ([σ|X′, X], ε, ε, [β|X′, X], P(X)) 
TER(x) ([σ|X′], ε, x, [β|X′], P(X′)) ⇒ ([σ|X′, x], ε, ε, [β|X′, x], P(X′)) 
RED ([σ|X′, X, x], ε, ε, [β|X′, X], P(X)) ⇒ ([σ|X′, X(x)], ε, ε, [β|X′], P(X′)) 
  
 Bottom–up Transitions
TER(x) (σ, ε, x) ⇒ ([σ|x], ε, ε) 
NT-RED(X) ([σ|x], X, ε) ⇒ ([σ|X(x)], ε, ε) 
 Top–down Transitions
NT(X) ([σ|X′], X, ε, [β|X′], P(X′)) ⇒ ([σ|X′, X], ε, ε, [β|X′, X], P(X)) 
TER(x) ([σ|X′], ε, x, [β|X′], P(X′)) ⇒ ([σ|X′, x], ε, ε, [β|X′, x], P(X′)) 
RED ([σ|X′, X, x], ε, ε, [β|X′, X], P(X)) ⇒ ([σ|X′, X(x)], ε, ε, [β|X′], P(X′)) 
  
 Bottom–up Transitions
TER(x) (σ, ε, x) ⇒ ([σ|x], ε, ε) 
NT-RED(X) ([σ|x], X, ε) ⇒ ([σ|X(x)], ε, ε) 
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