141 research outputs found
Parameterised Pushdown Systems with Non-Atomic Writes
We consider the master/slave parameterised reachability problem for networks
of pushdown systems, where communication is via a global store using only
non-atomic reads and writes. We show that the control-state reachability
problem is decidable. As part of the result, we provide a constructive
extension of a theorem by Ehrenfeucht and Rozenberg to produce an NFA
equivalent to certain kinds of CFG. Finally, we show that the non-parameterised
version is undecidable.Comment: This is the long version of a paper appearing in FSTTCS 201
Generating Concurrency Checks Automatically
This article introduces ATAB, a tool that automatically generates pairwise
reachability checks for action trees. Action trees can be used to study the
behaviour of real-world concurrent programs. ATAB encodes pairwise reachability
checks into alternating tree automata that determine whether an action tree has
a schedule where any pair of given points in the program are simultaneously
reachable. Because the pairwise reachability problem is undecidable in general
ATAB operates under a restricted form of lock-based concurrency. ATAB produces
alternating tree automata that are more compact and more efficiently checkable
than those that have been previously used. The process is entirely automated,
which simplifies the process of encoding checks for more complex action trees.
The alternating tree automata produced are easier to scale to large numbers of
locks than previous constructions.Comment: 15 pages, 9 figure
Optimal Strategies in Pushdown Reachability Games
An algorithm for computing optimal strategies in pushdown reachability games was given by Cachat. We show that the information tracked by this algorithm is too coarse and the strategies constructed are not necessarily optimal. We then show that the algorithm can be refined to recover optimality. Through a further non-trivial argument the refined algorithm can be run in 2EXPTIME by bounding the play-lengths tracked to those that are at most doubly exponential. This is optimal in the sense that there exists a game for which the optimal strategy requires a doubly exponential number of moves to reach a target configuration
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
Domains for Higher-Order Games
We study two-player inclusion games played over word-generating higher-order
recursion schemes. While inclusion checks are known to capture verification
problems, two-player games generalize this relationship to program synthesis.
In such games, non-terminals of the grammar are controlled by opposing players.
The goal of the existential player is to avoid producing a word that lies
outside of a regular language of safe words.
We contribute a new domain that provides a representation of the winning
region of such games. Our domain is based on (functions over) potentially
infinite Boolean formulas with words as atomic propositions. We develop an
abstract interpretation framework that we instantiate to abstract this domain
into a domain where the propositions are replaced by states of a finite
automaton. This second domain is therefore finite and we obtain, via standard
fixed-point techniques, a direct algorithm for the analysis of two-player
inclusion games. We show, via a second instantiation of the framework, that our
finite domain can be optimized, leading to a (k+1)EXP algorithm for order-k
recursion schemes. We give a matching lower bound, showing that our approach is
optimal. Since our approach is based on standard Kleene iteration, existing
techniques and tools for fixed-point computations can be applied.Comment: Conference version accepted for presentation and publication at the
42nd International Symposium on Mathematical Foundations of Computer Science
(MFCS 2017
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