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The potential of structural classification methods for automatic speech recognition (ASR) has been attracting the speech community since they can realize the unified modeling of acoustic and linguistic aspects of recognizers. However, the structural classification approaches involve well-known tradeoffs between the richness of features and the computational efficiency of decoders. If we are to employ, for example, a frame-synchronous one-pass decoding technique, features considered to calculate the likelihood of each hypothesis must be restricted to the same form as the conventional acoustic and language models. This paper tackles this limitation directly by exploiting the structure of the weighted finite-state transducers (WFSTs) used for decoding. Although WFST arcs provide rich contextual information, close integration with a computationally efficient decoding technique is still possible since most decoding techniques only require that their likelihood functions are factorizable for each decoder arc and time frame. In this paper, we compare two methods for structural classification with the WFST-based features; the structured perceptron and conditional random field (CRF) techniques. To analyze the advantages of these two classifiers, we present experimental results for the TIMIT continuous phoneme recognition task, the WSJ transcription task, and the MIT lecture transcription task. We confirmed that the proposed approach improved the ASR performance without sacrificing the computational efficiency of the decoders, even though the baseline systems are already trained with discriminative training techniques (e.g., MPE).