2,971 research outputs found
Folk Theorems on the Correspondence between State-Based and Event-Based Systems
Kripke Structures and Labelled Transition Systems are the two most prominent
semantic models used in concurrency theory. Both models are commonly believed
to be equi-expressive. One can find many ad-hoc embeddings of one of these
models into the other. We build upon the seminal work of De Nicola and
Vaandrager that firmly established the correspondence between stuttering
equivalence in Kripke Structures and divergence-sensitive branching
bisimulation in Labelled Transition Systems. We show that their embeddings can
also be used for a range of other equivalences of interest, such as strong
bisimilarity, simulation equivalence, and trace equivalence. Furthermore, we
extend the results by De Nicola and Vaandrager by showing that there are
additional translations that allow one to use minimisation techniques in one
semantic domain to obtain minimal representatives in the other semantic domain
for these equivalences.Comment: Full version of SOFSEM 2011 pape
Sequent Calculus in the Topos of Trees
Nakano's "later" modality, inspired by G\"{o}del-L\"{o}b provability logic,
has been applied in type systems and program logics to capture guarded
recursion. Birkedal et al modelled this modality via the internal logic of the
topos of trees. We show that the semantics of the propositional fragment of
this logic can be given by linear converse-well-founded intuitionistic Kripke
frames, so this logic is a marriage of the intuitionistic modal logic KM and
the intermediate logic LC. We therefore call this logic
. We give a sound and cut-free complete sequent
calculus for via a strategy that decomposes
implication into its static and irreflexive components. Our calculus provides
deterministic and terminating backward proof-search, yields decidability of the
logic and the coNP-completeness of its validity problem. Our calculus and
decision procedure can be restricted to drop linearity and hence capture KM.Comment: Extended version, with full proof details, of a paper accepted to
FoSSaCS 2015 (this version edited to fix some minor typos
Modal logic of planar polygons
We study the modal logic of the closure algebra , generated by the set
of all polygons in the Euclidean plane . We show that this logic
is finitely axiomatizable, is complete with respect to the class of frames we
call "crown" frames, is not first order definable, does not have the Craig
interpolation property, and its validity problem is PSPACE-complete
Verifying Temporal Regular Properties of Abstractions of Term Rewriting Systems
The tree automaton completion is an algorithm used for proving safety
properties of systems that can be modeled by a term rewriting system. This
representation and verification technique works well for proving properties of
infinite systems like cryptographic protocols or more recently on Java Bytecode
programs. This algorithm computes a tree automaton which represents a (regular)
over approximation of the set of reachable terms by rewriting initial terms.
This approach is limited by the lack of information about rewriting relation
between terms. Actually, terms in relation by rewriting are in the same
equivalence class: there are recognized by the same state in the tree
automaton.
Our objective is to produce an automaton embedding an abstraction of the
rewriting relation sufficient to prove temporal properties of the term
rewriting system.
We propose to extend the algorithm to produce an automaton having more
equivalence classes to distinguish a term or a subterm from its successors
w.r.t. rewriting. While ground transitions are used to recognize equivalence
classes of terms, epsilon-transitions represent the rewriting relation between
terms. From the completed automaton, it is possible to automatically build a
Kripke structure abstracting the rewriting sequence. States of the Kripke
structure are states of the tree automaton and the transition relation is given
by the set of epsilon-transitions. States of the Kripke structure are labelled
by the set of terms recognized using ground transitions. On this Kripke
structure, we define the Regular Linear Temporal Logic (R-LTL) for expressing
properties. Such properties can then be checked using standard model checking
algorithms. The only difference between LTL and R-LTL is that predicates are
replaced by regular sets of acceptable terms
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