76,695 research outputs found
The Complexity of Prenex Separation Logic with One Selector
We first show that infinite satisfiability can be reduced to finite
satisfiability for all prenex formulas of Separation Logic with
selector fields (\seplogk{k}). Second, we show that this entails the
decidability of the finite and infinite satisfiability problem for the class of
prenex formulas of \seplogk{1}, by reduction to the first-order theory of one
unary function symbol and unary predicate symbols. We also prove that the
complexity is not elementary, by reduction from the first-order theory of one
unary function symbol. Finally, we prove that the Bernays-Sch\"onfinkel-Ramsey
fragment of prenex \seplogk{1} formulae with quantifier prefix in the
language is \pspace-complete. The definition of a complete
(hierarchical) classification of the complexity of prenex \seplogk{1},
according to the quantifier alternation depth is left as an open problem
Inquisitive bisimulation
Inquisitive modal logic InqML is a generalisation of standard Kripke-style
modal logic. In its epistemic incarnation, it extends standard epistemic logic
to capture not just the information that agents have, but also the questions
that they are interested in. Technically, InqML fits within the family of
logics based on team semantics. From a model-theoretic perspective, it takes us
a step in the direction of monadic second-order logic, as inquisitive modal
operators involve quantification over sets of worlds. We introduce and
investigate the natural notion of bisimulation equivalence in the setting of
InqML. We compare the expressiveness of InqML and first-order logic in the
context of relational structures with two sorts, one for worlds and one for
information states. We characterise inquisitive modal logic, as well as its
multi-agent epistemic S5-like variant, as the bisimulation invariant fragment
of first-order logic over various natural classes of two-sorted structures.
These results crucially require non-classical methods in studying bisimulation
and first-order expressiveness over non-elementary classes of structures,
irrespective of whether we aim for characterisations in the sense of classical
or of finite model theory
Decidability Results for the Boundedness Problem
We prove decidability of the boundedness problem for monadic least
fixed-point recursion based on positive monadic second-order (MSO) formulae
over trees. Given an MSO-formula phi(X,x) that is positive in X, it is
decidable whether the fixed-point recursion based on phi is spurious over the
class of all trees in the sense that there is some uniform finite bound for the
number of iterations phi takes to reach its least fixed point, uniformly across
all trees. We also identify the exact complexity of this problem. The proof
uses automata-theoretic techniques. This key result extends, by means of
model-theoretic interpretations, to show decidability of the boundedness
problem for MSO and guarded second-order logic (GSO) over the classes of
structures of fixed finite tree-width. Further model-theoretic transfer
arguments allow us to derive major known decidability results for boundedness
for fragments of first-order logic as well as new ones
Bisimulation in Inquisitive Modal Logic
Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style
modal logic. In its epistemic incarnation, it extends standard epistemic logic
to capture not just the information that agents have, but also the questions
that they are interested in. Technically, InqML fits within the family of
logics based on team semantics. From a model-theoretic perspective, it takes us
a step in the direction of monadic second-order logic, as inquisitive modal
operators involve quantification over sets of worlds. We introduce and
investigate the natural notion of bisimulation equivalence in the setting of
InqML. We compare the expressiveness of InqML and first-order logic, and
characterise inquisitive modal logic as the bisimulation invariant fragments of
first-order logic over various classes of two-sorted relational structures.
These results crucially require non-classical methods in studying bisimulations
and first-order expressiveness over non-elementary classes.Comment: In Proceedings TARK 2017, arXiv:1707.0825
Infinite Networks, Halting and Local Algorithms
The immediate past has witnessed an increased amount of interest in local
algorithms, i.e., constant time distributed algorithms. In a recent survey of
the topic (Suomela, ACM Computing Surveys, 2013), it is argued that local
algorithms provide a natural framework that could be used in order to
theoretically control infinite networks in finite time. We study a
comprehensive collection of distributed computing models and prove that if
infinite networks are included in the class of structures investigated, then
every universally halting distributed algorithm is in fact a local algorithm.
To contrast this result, we show that if only finite networks are allowed, then
even very weak distributed computing models can define nonlocal algorithms that
halt everywhere. The investigations in this article continue the studies in the
intersection of logic and distributed computing initiated in (Hella et al.,
PODC 2012) and (Kuusisto, CSL 2013).Comment: In Proceedings GandALF 2014, arXiv:1408.556
On relating CTL to Datalog
CTL is the dominant temporal specification language in practice mainly due to
the fact that it admits model checking in linear time. Logic programming and
the database query language Datalog are often used as an implementation
platform for logic languages. In this paper we present the exact relation
between CTL and Datalog and moreover we build on this relation and known
efficient algorithms for CTL to obtain efficient algorithms for fragments of
stratified Datalog. The contributions of this paper are: a) We embed CTL into
STD which is a proper fragment of stratified Datalog. Moreover we show that STD
expresses exactly CTL -- we prove that by embedding STD into CTL. Both
embeddings are linear. b) CTL can also be embedded to fragments of Datalog
without negation. We define a fragment of Datalog with the successor build-in
predicate that we call TDS and we embed CTL into TDS in linear time. We build
on the above relations to answer open problems of stratified Datalog. We prove
that query evaluation is linear and that containment and satisfiability
problems are both decidable. The results presented in this paper are the first
for fragments of stratified Datalog that are more general than those containing
only unary EDBs.Comment: 34 pages, 1 figure (file .eps
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