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...Succinct graph representations of calculus formulas clemens kupke university strathclyde scotland johannes marti amsterdam the netherlands yde venema abstract manyalgorithmicresults on modal mu use such as alternating tree automata or hierarchical equation systems at closer inspection these results are not always optimal since exact relation between formula and its representation is clearly understood in particular there has been confusion about denition fundamental notion size a wepropose parity natural way representing yardstick for measuring complexity we discuss close connection this concept with games show that well known measures correspond to using syntax subformula closure respectively building work by bruse friedmann lange argue one needs thus dene terms fischer ladner new observation common assumption being clean every variable bound most incurs an exponential blow up realise upper model checking all our main result provide construction based given b preserves alternation dep...