2,761 research outputs found
Model-Checking Branching-Time Properties of Stateless Probabilistic Pushdown Systems and Its Quantum Extension
In this work, we first resolve a question in the probabilistic verification
of infinite-state systems (specifically, the probabilistic pushdown systems).
We show that model checking stateless probabilistic pushdown systems (pBPA)
against probabilistic computational tree logic (PCTL) is generally undecidable.
We define the quantum analogues of the probabilistic pushdown systems and
Markov chains and investigate whether it is necessary to define a quantum
analogue of probabilistic computational tree logic to describe the
branching-time properties of the quantum Markov chain. We also study its
model-checking problem and show that the model-checking of stateless quantum
pushdown systems (qBPA) against probabilistic computational tree logic (PCTL)
is generally undecidable, too.
The immediate corollaries of the above results are summarized in the work.Comment: Obvious typos corrected in new version; this work is a quantum
extension of arXiv:1405.4806, [v13]; 30 pages; comments are welcom
Enriched MU-Calculi Module Checking
The model checking problem for open systems has been intensively studied in
the literature, for both finite-state (module checking) and infinite-state
(pushdown module checking) systems, with respect to Ctl and Ctl*. In this
paper, we further investigate this problem with respect to the \mu-calculus
enriched with nominals and graded modalities (hybrid graded Mu-calculus), in
both the finite-state and infinite-state settings. Using an automata-theoretic
approach, we show that hybrid graded \mu-calculus module checking is solvable
in exponential time, while hybrid graded \mu-calculus pushdown module checking
is solvable in double-exponential time. These results are also tight since they
match the known lower bounds for Ctl. We also investigate the module checking
problem with respect to the hybrid graded \mu-calculus enriched with inverse
programs (Fully enriched \mu-calculus): by showing a reduction from the domino
problem, we show its undecidability. We conclude with a short overview of the
model checking problem for the Fully enriched Mu-calculus and the fragments
obtained by dropping at least one of the additional constructs
Global model checking on pushdown multi-agent systems
Pushdown multi-agent systems, modeled by pushdown game structures (PGSs), are an important paradigm of infinite-state multi-agent systems. Alternating-time temporal logics are well-known specification formalisms for multi-agent systems, where the selective path quantifier is introduced to reason about strategies of agents. In this paper, we investigate model checking algorithms for variants of alternating-time temporal logics over PGSs, initiated by Murano and Perelli at IJCAI'15. We first give a triply exponential-time model checking algorithm for ATL* over PGSs. The algorithm is based on the saturation method, and is the first global model checking algorithm with a matching lower bound. Next, we study the model checking problem for the alternating-time mu-calculus. We propose an exponential-time global model checking algorithm which extends similar algorithms for pushdown systems and modal mu-calculus. The algorithm admits a matching lower bound, which holds even for the alternation-free fragment and ATL
CARET analysis of multithreaded programs
Dynamic Pushdown Networks (DPNs) are a natural model for multithreaded
programs with (recursive) procedure calls and thread creation. On the other
hand, CARET is a temporal logic that allows to write linear temporal formulas
while taking into account the matching between calls and returns. We consider
in this paper the model-checking problem of DPNs against CARET formulas. We
show that this problem can be effectively solved by a reduction to the
emptiness problem of B\"uchi Dynamic Pushdown Systems. We then show that CARET
model checking is also decidable for DPNs communicating with locks. Our results
can, in particular, be used for the detection of concurrent malware.Comment: Pre-proceedings paper presented at the 27th International Symposium
on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur,
Belgium, 10-12 October 2017 (arXiv:1708.07854
Module Checking of Pushdown Multi-agent Systems
In this paper, we investigate the module-checking problem of pushdown multi-agent systems (PMS) against ATL and ATL* specifications. We establish that for ATL, module checking of PMS is 2EXPTIME-complete, which is the same complexity as pushdown module-checking for CTL. On the other hand, we show that ATL* module-checking of PMS turns out to be 4EXPTIME-complete, hence exponentially harder than both CTL* pushdown module-checking and ATL* model-checking of PMS. Our result for ATL* provides a rare example of a natural decision problem that is elementary yet but with a complexity that is higher than triply exponential-time
Module checking of pushdown multi-agent systems
In this paper, we investigate the module-checking problem of pushdown
multi-agent systems (PMS) against ATL and ATL* specifications. We establish
that for ATL, module checking of PMS is 2EXPTIME-complete, which is the same
complexity as pushdown module-checking for CTL. On the other hand, we show that
ATL* module-checking of PMS turns out to be 4EXPTIME-complete, hence
exponentially harder than both CTL* pushdown module-checking and ATL*
model-checking of PMS. Our result for ATL* provides a rare example of a natural
decision problem that is elementary yet but with a complexity that is higher
than triply exponential-time.Comment: arXiv admin note: substantial text overlap with arXiv:1709.0210
A Navigation Logic for Recursive Programs with Dynamic Thread Creation
Dynamic Pushdown Networks (DPNs) are a model for multithreaded programs with
recursion and dynamic creation of threads. In this paper, we propose a temporal
logic called NTL for reasoning about the call- and return- as well as thread
creation behaviour of DPNs. Using tree automata techniques, we investigate the
model checking problem for the novel logic and show that its complexity is not
higher than that of LTL model checking against pushdown systems despite a more
expressive logic and a more powerful system model. The same holds true for the
satisfiability problem when compared to the satisfiability problem for a
related logic for reasoning about the call- and return-behaviour of pushdown
systems. Overall, this novel logic offers a promising approach for the
verification of recursive programs with dynamic thread creation
- …