We present in this paper a series of languages adequate for expressing exactly those properties checkable in a series of computational complexity classes For example we show that a property of graphs respectively groups binary strings etc is in polynomial time if and only if it is expressible in the rst order language of graphs respectively groups binary strings etc together with a least xed point operator As another example a property is in logspace if and only if it is expressible in rstâ€¦Â CONTINUE READING