(a) for property acquired by a state public authority or by the state for the purposes of a state public authority, such transition assessments shall be reduced to take into account any payments in lieu of taxes made pursuant to law by such state public authority to the tax district, so that the total of state aid paid on each transition assessment and the payment in lieu of taxes received by the tax district would be in effect equal to the state aid payable on such transition assessment computed without regard to this subdivision; and

(b) for state lands in which interests have been granted by the state to others which interests and improvements made to lands in which those interests have been granted are taxable pursuant to subdivision two of section five hundred sixty-four of this article, such transition assessments shall be reduced by the taxable assessed value of those interests and improvements.

(c) The assessor in each assessing unit for which transition assessments are made pursuant to this section shall annually report to the commissioner the total taxable assessed value of interests and improvements subject to taxation pursuant to subdivision two of section five hundred sixty-four of this article. This report shall be filed not later than ten days after the completion and filing of the final assessment roll each year. 7. Definitions. As used in this section: a. "Agency of the state", in the case of public authorities, includes state public authorities but excludes all other public authorities. b. "Assessment roll", in the case of a city or town, means the entire city or town assessment roll; in the case of a village, means the entire village assessment roll, except in the case of a village which has enacted a local law as provided in subdivision three of section fourteen hundred two of this chapter, may also mean that part of the assessment roll of the town or county upon which village taxes were or are to be levied; in the case of a county, means the entire city or town assessment roll affected by the occurrence or occurrences described in subdivision one of this section; in the case of a school district or special district, means that portion of the city or town assessment roll used for the levy of school or special district taxes which is affected by the occurrence. c. "First year" means a year following a year for which no transition assessment was established. d. "Lands" or "state lands" as used in this section, shall include lands acquired by the state or an agency of the state for highway or parkway purposes. e. "Latest preceding assessment roll" means the last preceding assessment roll finally completed, verified and filed prior to the final completion of the assessment roll for which the transition assessment is being established, but shall not mean or include a supplemental assessment roll completed, verified and filed as provided in section thirteen hundred thirty-five of this chapter. f. "Reduction in assessments on state lands" means a loss in taxable assessed valuation on an assessment roll as a result of the approval by the commissioner of assessed valuations on state lands which in total amount to less than the total taxable assessed valuations on such lands in the preceding year, whether or not such lands were owned by the state in the preceding year. g. "State public authority" means a public benefit corporation as defined in section sixty-six of the general construction law whose membership is required by law to consist entirely of members who are appointed by the governor or other state officer or who serve as members as ex officio state officers. h. "Tax district" means a county, city, town, village, school district or special district.