Abstract Statistics of Morphological Finite-State Transition Networks Obey the.pdfVIP

Statistics of Morphological Finite-State Transition Networks Obey the Power Law Alexander Troussov, Brian O’Donovan IBM Dublin Software Lab, Airways Ind. Est., Cloghran, Dublin 17, Ireland {atrousso, Brian_ODonovan}@ Abstract Finite-state devices are widely used in natural lan- guage processing, yet little if anything is known about metrics and topology of finite-state transition graphs. Here we study numerically the structure of directed state transition graphs for several types of finite-state devices representing morphology of 16 languages. In all experiments we have found that distribution of in- coming and outcoming links is highly skewed and is modeled well by the power law, not by Poisson distri- bution typical of classical random graphs. The power- law form of degree distribution is regarded as a signa- ture of self-organizing systems, and it has been previ- ously found for numerous real world networks in communication, biology, social sciences and econom- ics. 1 Introduction Finite-state devices, including finite-state automata and transducers, are widely used in natural language processing to produce morphological information. Constructed as applications of formal finite-state techniques, they can be considered as networks where nodes represent states and arcs (labeled by characters) represent the transitions. Examination of their graph- metrics and topology is essential for efficient com- puter implementation of finite-state processing, in- cluding per-node optimization. It might also lead to new quantitative methods in language typology as we argue below. In computational linguistics semantic and co- occurrence networks were already studied. In these networks nodes correspond to words. In semantic networks the links show semantic relations between words. In co-occurrence networks links represent the fact that words occur beside each other in a corpus. We are not aware of similar investigations applied to finite-state t