68 research outputs found
Necessary and Sufficient Conditions on Partial Orders for Modeling Concurrent Computations
Partial orders are used extensively for modeling and analyzing concurrent
computations. In this paper, we define two properties of partially ordered
sets: width-extensibility and interleaving-consistency, and show that a partial
order can be a valid state based model: (1) of some synchronous concurrent
computation iff it is width-extensible, and (2) of some asynchronous concurrent
computation iff it is width-extensible and interleaving-consistent. We also
show a duality between the event based and state based models of concurrent
computations, and give algorithms to convert models between the two domains.
When applied to the problem of checkpointing, our theory leads to a better
understanding of some existing results and algorithms in the field. It also
leads to efficient detection algorithms for predicates whose evaluation
requires knowledge of states from all the processes in the system
The complexity of Boolean surjective general-valued CSPs
Valued constraint satisfaction problems (VCSPs) are discrete optimisation
problems with a -valued objective function given as
a sum of fixed-arity functions. In Boolean surjective VCSPs, variables take on
labels from and an optimal assignment is required to use both
labels from . Examples include the classical global Min-Cut problem in
graphs and the Minimum Distance problem studied in coding theory.
We establish a dichotomy theorem and thus give a complete complexity
classification of Boolean surjective VCSPs with respect to exact solvability.
Our work generalises the dichotomy for -valued constraint
languages (corresponding to surjective decision CSPs) obtained by Creignou and
H\'ebrard. For the maximisation problem of -valued
surjective VCSPs, we also establish a dichotomy theorem with respect to
approximability.
Unlike in the case of Boolean surjective (decision) CSPs, there appears a
novel tractable class of languages that is trivial in the non-surjective
setting. This newly discovered tractable class has an interesting mathematical
structure related to downsets and upsets. Our main contribution is identifying
this class and proving that it lies on the borderline of tractability. A
crucial part of our proof is a polynomial-time algorithm for enumerating all
near-optimal solutions to a generalised Min-Cut problem, which might be of
independent interest.Comment: v5: small corrections and improved presentatio
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