28,180 research outputs found
Lean and Full Congruence Formats for Recursion
In this paper I distinguish two (pre)congruence requirements for semantic
equivalences and preorders on processes given as closed terms in a system
description language with a recursion construct. A lean congruence preserves
equivalence when replacing closed subexpressions of a process by equivalent
alternatives. A full congruence moreover allows replacement within a recursive
specification of subexpressions that may contain recursion variables bound
outside of these subexpressions.
I establish that bisimilarity is a lean (pre)congruence for recursion for all
languages with a structural operational semantics in the ntyft/ntyxt format.
Additionally, it is a full congruence for the tyft/tyxt format.Comment: To appear in: Proc. LICS'17, Reykjavik, Iceland, IEE
Tree rules in probabilistic transition system specifications with negative and quantitative premises
Probabilistic transition system specifications (PTSSs) in the ntmufnu/ntmuxnu
format provide structural operational semantics for Segala-type systems that
exhibit both probabilistic and nondeterministic behavior and guarantee that
isimilarity is a congruence.Similar to the nondeterministic case of rule format
tyft/tyxt, we show that the well-foundedness requirement is unnecessary in the
probabilistic setting. To achieve this, we first define an extended version of
the ntmufnu/ntmuxnu format in which quantitative premises and conclusions
include nested convex combinations of distributions. This format also
guarantees that bisimilarity is a congruence. Then, for a given (possibly
non-well-founded) PTSS in the new format, we construct an equivalent
well-founded transition system consisting of only rules of the simpler
(well-founded) probabilistic ntree format. Furthermore, we develop a
proof-theoretic notion for these PTSSs that coincides with the existing
stratification-based meaning in case the PTSS is stratifiable. This continues
the line of research lifting structural operational semantic results from the
nondeterministic setting to systems with both probabilistic and
nondeterministic behavior.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244
A general conservative extension theorem in process algebras with inequalities
We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity, that is, provable transitions from an original term in the extension are the same as in the original system. As a simple corollary of the conservative extension theorem we prove a completeness theorem. We also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one. We provide many applications to show that our results are useful. The applications include (but are not limited to) various real and discrete time settings in ACP, ATP, and CCS and the notions projection, renaming, stage operator, priority, recursion, the silent step, autonomous actions, the empty process, divergence, etc
SOS rule formats for convex and abstract probabilistic bisimulations
Probabilistic transition system specifications (PTSSs) in the format provide structural operational semantics for
Segala-type systems that exhibit both probabilistic and nondeterministic
behavior and guarantee that bisimilarity is a congruence for all operator
defined in such format. Starting from the
format, we obtain restricted formats that guarantee that three coarser
bisimulation equivalences are congruences. We focus on (i) Segala's variant of
bisimulation that considers combined transitions, which we call here "convex
bisimulation"; (ii) the bisimulation equivalence resulting from considering
Park & Milner's bisimulation on the usual stripped probabilistic transition
system (translated into a labelled transition system), which we call here
"probability obliterated bisimulation"; and (iii) a "probability abstracted
bisimulation", which, like bisimulation, preserves the structure of the
distributions but instead, it ignores the probability values. In addition, we
compare these bisimulation equivalences and provide a logic characterization
for each of them.Comment: In Proceedings EXPRESS/SOS 2015, arXiv:1508.0634
Causality in the Semantics of Esterel: Revisited
We re-examine the challenges concerning causality in the semantics of Esterel
and show that they pertain to the known issues in the semantics of Structured
Operational Semantics with negative premises. We show that the solutions
offered for the semantics of SOS also provide answers to the semantic
challenges of Esterel and that they satisfy the intuitive requirements set by
the language designers
Meta SOS - A Maude Based SOS Meta-Theory Framework
Meta SOS is a software framework designed to integrate the results from the
meta-theory of structural operational semantics (SOS). These results include
deriving semantic properties of language constructs just by syntactically
analyzing their rule-based definition, as well as automatically deriving sound
and ground-complete axiomatizations for languages, when considering a notion of
behavioural equivalence. This paper describes the Meta SOS framework by
blending aspects from the meta-theory of SOS, details on their implementation
in Maude, and running examples.Comment: In Proceedings EXPRESS/SOS 2013, arXiv:1307.690
Distributive Laws and Decidable Properties of SOS Specifications
Some formats of well-behaved operational specifications, correspond to
natural transformations of certain types (for example, GSOS and coGSOS laws).
These transformations have a common generalization: distributive laws of monads
over comonads. We prove that this elegant theoretical generalization has
limited practical benefits: it does not translate to any concrete rule format
that would be complete for specifications that contain both GSOS and coGSOS
rules. This is shown for the case of labeled transition systems and
deterministic stream systems.Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127
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