TY - JOUR
T1 - Elimination of quantifiers and undecidability in spatial logics for concurrency
AU - Caires, Luís
AU - Lozes, Etienne
N1 - We thank Hongseok Yang for the illuminating discussion that prompted our counterexample in Section 4. We acknowledge Luís Monteiro, Daniel Hirschkoff and Davide Sangiorgi for all the rich exchanges and encouragement; and Luca Cardelli for many related discussions. E. Jeandel provided some references about quantifier elimination. This collaboration was supported by FET IST 2001-33310 Profundis. E. Lozes was also funded by an “Eurodoc” grant from Région Rhône Alpes.
PY - 2006/8/7
Y1 - 2006/8/7
N2 - The introduction of spatial logics in concurrency is motivated by a shift of focus from concurrent systems towards distributed systems. Aiming at a deeper understanding of the essence of dynamic spatial logics, we study a minimal spatial logic without quantifiers or any operators talking about names. The logic just includes the basic spatial operators void, composition and its adjunct, and the next step modality; for the model we consider a tiny fragment of CCS. We show that this core logic can already encode its own extension with quantification over actions, and modalities for actions. From this result, we derive several consequences. Firstly, we establish the intensionality of the logic, we characterize the equivalence it induces on processes, and we derive characteristic formulas. Secondly, we show that, unlike in static spatial logics, the composition adjunct adds to the expressiveness of the logic, so that adjunct elimination is not possible for dynamic spatial logics, even quantifier-free. Finally, we prove that both model-checking and satisfiability problems are undecidable in our logic. We also conclude that our results extend to other calculi, namely the π-calculus and the ambient calculus.
AB - The introduction of spatial logics in concurrency is motivated by a shift of focus from concurrent systems towards distributed systems. Aiming at a deeper understanding of the essence of dynamic spatial logics, we study a minimal spatial logic without quantifiers or any operators talking about names. The logic just includes the basic spatial operators void, composition and its adjunct, and the next step modality; for the model we consider a tiny fragment of CCS. We show that this core logic can already encode its own extension with quantification over actions, and modalities for actions. From this result, we derive several consequences. Firstly, we establish the intensionality of the logic, we characterize the equivalence it induces on processes, and we derive characteristic formulas. Secondly, we show that, unlike in static spatial logics, the composition adjunct adds to the expressiveness of the logic, so that adjunct elimination is not possible for dynamic spatial logics, even quantifier-free. Finally, we prove that both model-checking and satisfiability problems are undecidable in our logic. We also conclude that our results extend to other calculi, namely the π-calculus and the ambient calculus.
KW - Concurrency
KW - Expressiveness
KW - Spatial logic
KW - Undecidability
UR - http://www.scopus.com/inward/record.url?scp=33746287259&partnerID=8YFLogxK
U2 - 10.1016/j.tcs.2006.01.020
DO - 10.1016/j.tcs.2006.01.020
M3 - Article
AN - SCOPUS:33746287259
VL - 358
SP - 293
EP - 314
JO - Theoretical Computer Science
JF - Theoretical Computer Science
SN - 0304-3975
IS - 2-3
T2 - 15th International Conference on Concurrency Theory
Y2 - 31 August 2004 through 3 September 2004
ER -