Verifiable and executable logic specifications of concurrent objects in $$\mathcal{L}_\pi$$

Caires, Luís; Monteiro, Luís

doi:10.1007/bfb0053562

Cited by 8 publications

(10 citation statements)

References 19 publications

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“…In a spatial logic, the truth of a formula depends on a spatial structure, such as a system of ambients. Apart from the ambient logic, other examples include logics for concurrent objects [4], heaps [25,20,22], trees [6], graphs [5], and the π-calculus [2,3]. Spatial logics are being applied as notations for specifying and verifying programs, and as query languages for semistructured data.…”

Section: Resultsmentioning

confidence: 99%

“…Now, the closure P ; σ being normal, if I contains at least two elements then by definition of U, U(P , σ) ≡ R | R for some R, R ≡ 0 by Propositions C.5 and C. 4 . Thus, still by Proposition C. 4…”

Section: Proofmentioning

confidence: 99%

“…Now, by Proposition C.9, we know that fst(L , o, σ) = L. Thus, it is sufficient to prove that P ≡ U(P , σ) for split(π i , σ) = (L,P ). From the definitions of U and split and from Proposition C. 4, it is straightforward to see that P ≡ U(P , σ) implies U( i∈I π i , σ) ≡ L.P .…”

Section: Proofmentioning

confidence: 99%

“…Lemma D. 4 For all 0 ≤ m < n, P M → 2 (v m+1 [] | P ϕm+1 )σ M + and P M → 2 (v m+1 [] | P ϕm+1 )σ M − and there is no other P such that P → 2 P .…”

Section: Lemma D3mentioning

confidence: 99%

“…For instance, by Theorem 5. 4, even for a calculus of purely mobile ambients (that is, a calculus without communication or the capability to dissolve ambients) and the logic without quantifiers, the problem is PSPACE-hard. Moreover, by Theorem 5.6, for a calculus of purely communicative ambients (that is, a calculus without the capabilities to move or to dissolve ambients) and the logic without quantifiers, the problem is also PSPACE-hard.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The Decidability of Model Checking Mobile Ambients

Charatonik

Talbot

2001

Computer Science Logic

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We settle the complexity bounds of the model checking problem for the ambient calculus with public names against the ambient logic. We show that if either the calculus contains replication or the logic contains the guarantee operator, the problem is undecidable. In the case of the replication-free calculus and guarantee-free logic we prove that the problem is PSPACE-complete. For the complexity upper-bound, we devise a new representation of processes that remains of polynomial size during process execution; this allows us to keep the model checking procedure in polynomial space. Moreover, we prove PSPACE-hardness of the problem for several quite simple fragments of the calculus and the logic; this suggests that there are no interesting fragments with polynomial-time model checking algorithms.

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