4,826 research outputs found
Model checking Branching-Time Properties of Multi-Pushdown Systems is Hard
We address the model checking problem for shared memory concurrent programs
modeled as multi-pushdown systems. We consider here boolean programs with a
finite number of threads and recursive procedures. It is well-known that the
model checking problem is undecidable for this class of programs. In this
paper, we investigate the decidability and the complexity of this problem under
the assumption of bounded context-switching defined by Qadeer and Rehof, and of
phase-boundedness proposed by La Torre et al. On the model checking of such
systems against temporal logics and in particular branching time logics such as
the modal -calculus or CTL has received little attention. It is known that
parity games, which are closely related to the modal -calculus, are
decidable for the class of bounded-phase systems (and hence for bounded-context
switching as well), but with non-elementary complexity (Seth). A natural
question is whether this high complexity is inevitable and what are the ways to
get around it. This paper addresses these questions and unfortunately, and
somewhat surprisingly, it shows that branching model checking for MPDSs is
inherently an hard problem with no easy solution. We show that parity games on
MPDS under phase-bounding restriction is non-elementary. Our main result shows
that model checking a context bounded MPDS against a simple fragment of
CTL, consisting of formulas that whose temporal operators come from the set
{\EF, \EX}, has a non-elementary lower bound
Design evaluation of automated manufacturing processes based on complexity of control logic
Complexity continues to be a challenge in manufacturing systems, resulting in ever-inflating costs, operational issues and increased lead times to product realisation. Assessing complexity realizes the reduction and management of complexity sources which contributes to lowering associated engineering costs and time, improves productivity and increases profitability. This paper proposes an approach for evaluating the design of automated manufacturing processes based on the structural complexity of the control logic. Six complexity indices are introduced and formulated: Coupling, Restrictiveness, Diameter, Branching, Centralization, and Uncertainty. An overall Logical Complexity Index (CL) which combines all of these indices is developed and demonstrated using a simple pick and place automation process. The results indicate that the proposed approach can help design automation logics with the least complexity and compare alternatives that meet the requirements during initial design stages
The Complexity of Model Checking (Collapsible) Higher-Order Pushdown Systems
We study (collapsible) higher-order pushdown systems --- theoretically robust and well-studied models of higher-order programs --- along with their natural subclass called (collapsible) higher-order basic process algebras. We provide a comprehensive analysis of the model checking complexity of a range of both branching-time and linear-time temporal logics. We obtain tight bounds on data, expression, and combined-complexity for both (collapsible) higher-order pushdown systems and (collapsible) higher-order basic process algebra. At order-, results range from polynomial to -exponential time. Finally, we study (collapsible) higher-order basic process algebras as graph generators and show that they are almost as powerful as (collapsible) higher-order pushdown systems up to MSO interpretations
Quantified CTL: Expressiveness and Complexity
While it was defined long ago, the extension of CTL with quantification over
atomic propositions has never been studied extensively. Considering two
different semantics (depending whether propositional quantification refers to
the Kripke structure or to its unwinding tree), we study its expressiveness
(showing in particular that QCTL coincides with Monadic Second-Order Logic for
both semantics) and characterise the complexity of its model-checking and
satisfiability problems, depending on the number of nested propositional
quantifiers (showing that the structure semantics populates the polynomial
hierarchy while the tree semantics populates the exponential hierarchy)
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