5,754 research outputs found
On the Complexity of Elementary Modal Logics
Modal logics are widely used in computer science. The complexity of modal
satisfiability problems has been investigated since the 1970s, usually proving
results on a case-by-case basis. We prove a very general classification for a
wide class of relevant logics: Many important subclasses of modal logics can be
obtained by restricting the allowed models with first-order Horn formulas. We
show that the satisfiability problem for each of these logics is either
NP-complete or PSPACE-hard, and exhibit a simple classification criterion.
Further, we prove matching PSPACE upper bounds for many of the PSPACE-hard
logics.Comment: Full version of STACS 2008 pape
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
Why Does Propositional Quantification Make Modal and Temporal Logics on Trees Robustly Hard?
Adding propositional quantification to the modal logics K, T or S4 is known
to lead to undecidability but CTL with propositional quantification under the
tree semantics (tQCTL) admits a non-elementary Tower-complete satisfiability
problem. We investigate the complexity of strict fragments of tQCTL as well as
of the modal logic K with propositional quantification under the tree
semantics. More specifically, we show that tQCTL restricted to the temporal
operator EX is already Tower-hard, which is unexpected as EX can only enforce
local properties. When tQCTL restricted to EX is interpreted on N-bounded trees
for some N >= 2, we prove that the satisfiability problem is AExpPol-complete;
AExpPol-hardness is established by reduction from a recently introduced tiling
problem, instrumental for studying the model-checking problem for interval
temporal logics. As consequences of our proof method, we prove Tower-hardness
of tQCTL restricted to EF or to EXEF and of the well-known modal logics such as
K, KD, GL, K4 and S4 with propositional quantification under a semantics based
on classes of trees
Why Propositional Quantification Makes Modal Logics on Trees Robustly Hard?
International audienceAdding propositional quantification to the modal logics K, T or S4 is known to lead to undecid-ability but CTL with propositional quantification under the tree semantics (QCTL t) admits a non-elementary Tower-complete satisfiability problem. We investigate the complexity of strict fragments of QCTL t as well as of the modal logic K with propositional quantification under the tree semantics. More specifically, we show that QCTL t restricted to the temporal operator EX is already Tower-hard, which is unexpected as EX can only enforce local properties. When QCTL t restricted to EX is interpreted on N-bounded trees for some N ≥ 2, we prove that the satisfiability problem is AExp pol-complete; AExp pol-hardness is established by reduction from a recently introduced tiling problem, instrumental for studying the model-checking problem for interval temporal logics. As consequences of our proof method, we prove Tower-hardness of QCTL t restricted to EF or to EXEF and of the well-known modal logics K, KD, GL, S4, K4 and D4, with propositional quantification under a semantics based on classes of trees
Light Logics and the Call-by-Value Lambda Calculus
The so-called light logics have been introduced as logical systems enjoying
quite remarkable normalization properties. Designing a type assignment system
for pure lambda calculus from these logics, however, is problematic. In this
paper we show that shifting from usual call-by-name to call-by-value lambda
calculus allows regaining strong connections with the underlying logic. This
will be done in the context of Elementary Affine Logic (EAL), designing a type
system in natural deduction style assigning EAL formulae to lambda terms.Comment: 28 page
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