Expressivity within second-order transitive-closure logic

F. Ferrarotti, J. Van den Bussche, J. Virtema. Expressivity within second-order transitive-closure logic. volume 119, pages 22:1-22:18, DOI 10.4230/LIPIcs.CSL.2018.22, 9, 2018.

  • Flavio Ferrarotti
  • Jan Van den Bussche
  • Jonni Virtema
BuchProceedings of the 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)
TypIn Konferenzband
VerlagSchloss Dagstuhl-Leibniz-Zentrum für Informatik
SerieLeibniz International Proceedings in Informatics (LIPICS)

Second-order transitive-closure logic, SO(TC), is an expressive declarative language that captures the complexity class PSPACE. Already its monadic fragment, MSO(TC), allows the expression of various NP-hard and even PSPACE-hard problems in a natural and elegant manner. As SO(TC) offers an attractive framework for expressing properties in terms of declaratively specified computations, it is interesting to understand the expressivity of different features of the language. This paper focuses on the fragment MSO(TC), as well on the purely existential fragment SO(2TC)(exists); in 2TC, the TC operator binds only tuples of relation variables. We establish that, with respect to expressive power, SO(2TC)(exists) collapses to existential first-order logic. In addition we study the relationship of MSO(TC) to an extension of MSO(TC) with counting features (CMSO(TC)) as well as to order-invariant MSO. We show that the expressive powers of CMSO(TC) and MSO(TC) coincide. Moreover we establish that, over unary vocabularies, MSO(TC) strictly subsumes order-invariant MSO.