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This paper presents a bidirectional inference algorithm for sequence labeling problems such as part-of-speech tagging, named entity recognition and text chunking. The algorithm can enumerate all possible decomposition structures and find the highest probability sequence together with the corresponding decomposition structure in polynomial time. We also present an efficient decoding algorithm based on the easiest-first strategy, which gives comparably good performance to full bidirectional inference with significantly lower computational cost. Experimental results of part-of-speech tagging and text chunking show that the proposed bidirectional inference methods consistently outperform unidirectional inference methods and bidirectional MEMMs give comparable performance to that achieved by state-of-the-art learning algorithms including kernel support vector machines.