Indexed Languages and Unification Grammars

T h e occu rren ce o f purely syn tactica l cross-serial depen den cies in S w iss-G erm an show s that con text-free gram m ars can n ot describe the string sets o f natu ral lan­ guage [Shi85]. T h e least class in the C h om sk y hierarchy th at can d escribe u n lim ited cross-serial depen dencies is in dexed g ram m ars [A h o 68]. G azd a r discuss in [G a z88] the ap p licab ility o f in dexed gram m ars to natural languages, and show how th ey can be used to describe different sy n tactic structures. W e are here g o in g to stu d y h ow we can describe the class o f indexed languages w ith a u n ifica tion g ra m m a r form alism . A fter defin ing indexed gram m ars and a sim p le u n ifica tion g ra m m a r fram ew ork we show how we can define an equ ivalent u n ifica tion g ra m m a r for any g iven indexed gram m ar. T w o gram m ars are equ ivalent if they generate the sam e language. W ith this backgrou n d we define a class o f u n ifica tion gram m ars and show th at th is class describes the clciss o f indexed languages.