20 research outputs found
Unified Analysis of Collapsible and Ordered Pushdown Automata via Term Rewriting
We model collapsible and ordered pushdown systems with term rewriting, by
encoding higher-order stacks and multiple stacks into trees. We show a uniform
inverse preservation of recognizability result for the resulting class of term
rewriting systems, which is obtained by extending the classic saturation-based
approach. This result subsumes and unifies similar analyses on collapsible and
ordered pushdown systems. Despite the rich literature on inverse preservation
of recognizability for term rewrite systems, our result does not seem to follow
from any previous study.Comment: in Proc. of FRE
Reflections on a Geometry of Processes
Contains fulltext :
32919.pdf (publisher's version ) (Open Access)Algebraic Process Calcul
Synchronous Subsequentiality and Approximations to Undecidable Problems
We introduce the class of synchronous subsequential relations, a subclass of
the synchronous relations which embodies some properties of subsequential
relations. If we take relations of this class as forming the possible
transitions of an infinite automaton, then most decision problems (apart from
membership) still remain undecidable (as they are for synchronous and
subsequential rational relations), but on the positive side, they can be
approximated in a meaningful way we make precise in this paper. This might make
the class useful for some applications, and might serve to establish an
intermediate position in the trade-off between issues of expressivity and
(un)decidability.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
Turchin's Relation for Call-by-Name Computations: A Formal Approach
Supercompilation is a program transformation technique that was first
described by V. F. Turchin in the 1970s. In supercompilation, Turchin's
relation as a similarity relation on call-stack configurations is used both for
call-by-value and call-by-name semantics to terminate unfolding of the program
being transformed. In this paper, we give a formal grammar model of
call-by-name stack behaviour. We classify the model in terms of the Chomsky
hierarchy and then formally prove that Turchin's relation can terminate all
computations generated by the model.Comment: In Proceedings VPT 2016, arXiv:1607.0183
Modelchecking counting properties of 1-safe nets with buffers in paraPSPACE
We consider concurrent systems that can be modelled as -safe
Petri nets communicating through a fixed set of buffers (modelled as
unbounded places). We identify a parameter , which we call
``benefit depth\u27\u27, formed from the communication graph between the
buffers. We show that for our system model, the coverability and boundedness
problems can be solved in polynomial space assuming to be a
fixed parameter, that is, the space requirement is ,
where is an exponential function and is a polynomial in
the size of the input. We then obtain similar complexity bounds for
modelchecking a logic based on such counting properties.
This means that systems that have sparse communication patterns can
be analyzed more efficiently than using previously
known algorithms for general Petri nets
Boolean Algebras from Trace Automata
We consider trace automata. Their vertices are Mazurkiewicz traces and they accept finite words. Considering the length of a trace as the length of its Foata normal form, we define the operations of level-length synchronization and of superposition of trace automata. We show that if a family F of trace automata is closed under these operations, then for any deterministic automaton H in F, the word languages accepted by the deterministic automata of F that are length-reducible to H form a Boolean algebra. We show that the family of trace suffix automata with level-regular contexts and the subfamily of vector addition systems satisfy these closure properties. In particular, this yields various Boolean algebras of word languages accepted by deterministic vector addition systems
Recurrent Reachability Analysis in Regular Model Checking
Abstract. We consider the problem of recurrent reachability over infinite systems given by regular relations on words and trees, i.e, whether a given regular set of states can be reached infinitely often from a given initial state in the given transition system. Under the condition that the transitive closure of the transition relation is regular, we show that the problem is decidable, and the set of all initial states satisfying the property is regular. Moreover, our algorithm constructs an automaton for this set in polynomial time, assuming that a transducer of the transitive closure can be computed in poly-time. We then demonstrate that transition systems generated by pushdown systems, regular ground tree rewrite systems, and the well-known process algebra PA satisfy our condition and transducers for their transitive closures can be computed in poly-time. Our result also implies that model checking EF-logic extended by recurrent reachability predicate (EGF) over such systems is decidable.
Concurrency Makes Simple Theories Hard
A standard way of building concurrent systems is by composing several
individual processes by product operators. We show that even the simplest notion of product operators (i.e. asynchronous products) suffices to increase the complexity of model checking simple logics like Hennessy-Milner (HM) logic and its extension with the reachability operator (EF-logic) from PSPACE to nonelementary. In particular, this nonelementary jump happens for EF-logic when we consider individual processes represented by pushdown systems (indeed, even with only one control state). Using this result, we prove nonelementary lower bounds on the size of formula decompositions provided by Feferman-Vaught (de)compositional methods for HM and EF logics, which reduce theories of asynchronous products to theories of the components. Finally, we show that the same nonelementary lower bounds also hold when we consider the relativization of such compositional methods to finite systems
Equivalence-Checking on Infinite-State Systems: Techniques and Results
The paper presents a selection of recently developed and/or used techniques
for equivalence-checking on infinite-state systems, and an up-to-date overview
of existing results (as of September 2004)