892 research outputs found
Forward Analysis and Model Checking for Trace Bounded WSTS
We investigate a subclass of well-structured transition systems (WSTS), the
bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete
deterministic ones, which we claim provide an adequate basis for the study of
forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth.
Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered
previously for the termination of forward analysis, boundedness is decidable.
Boundedness turns out to be a valuable restriction for WSTS verification, as we
show that it further allows to decide all -regular properties on the
set of infinite traces of the system
Decidability Issues for Petri Nets
This is a survey of some decidability results for Petri nets, covering the last three decades. The presentation is structured around decidability of specific properties, various behavioural equivalences and finally the model checking problem for temporal logics
A polynomial-time algorithm for reachability in branching VASS in dimension one
Branching VASS (BVASS) generalise vector addition systems with states by allowing for special branching transitions that can non-deterministically distribute a counter value between two control states. A run of a BVASS consequently becomes a tree, and reachability is to decide whether a given configuration is the root of a reachability tree. This paper shows P-completeness of reachability in BVASS in dimension one, the first decidability result for reachability in a subclass of BVASS known so far. Moreover, we show that coverability and boundedness in BVASS in dimension one are P-complete as well
KReach : a tool for reachability in petri nets
We present KReach, a tool for deciding reachability in general Petri nets. The tool is a full implementation of Kosaraju’s original 1982 decision procedure for reachability in VASS. We believe this to be the first implementation of its kind. We include a comprehensive suite of libraries for development with Vector Addition Systems (with States) in the Haskell programming language. KReach serves as a practical tool, and acts as an effective teaching aid for the theory behind the algorithm. Preliminary tests suggest that there are some classes of Petri nets for which we can quickly show unreachability. In particular, using KReach for coverability problems, by reduction to reachability, is competitive even against state-of-the-art coverability checkers
Decidable Models of Recursive Asynchronous Concurrency
Asynchronously communicating pushdown systems (ACPS) that satisfy the
empty-stack constraint (a pushdown process may receive only when its stack is
empty) are a popular decidable model for recursive programs with asynchronous
atomic procedure calls. We study a relaxation of the empty-stack constraint for
ACPS that permits concurrency and communication actions at any stack height,
called the shaped stack constraint, thus enabling a larger class of concurrent
programs to be modelled. We establish a close connection between ACPS with
shaped stacks and a novel extension of Petri nets: Nets with Nested Coloured
Tokens (NNCTs). Tokens in NNCTs are of two types: simple and complex. Complex
tokens carry an arbitrary number of coloured tokens. The rules of NNCT can
synchronise complex and simple tokens, inject coloured tokens into a complex
token, and eject all tokens of a specified set of colours to predefined places.
We show that the coverability problem for NNCTs is Tower-complete. To our
knowledge, NNCT is the first extension of Petri nets, in the class of nets with
an infinite set of token types, that has primitive recursive coverability. This
result implies Tower-completeness of coverability for ACPS with shaped stacks
On the complexity of resource-bounded logics
We revisit decidability results for resource-bounded logics and use decision problems for vector addition systems with states (VASS) to characterise the complexity of (decidable) model-checking problems.
We show that the model-checking problem for the logic RB+-ATL is 2EXPTIME-complete by using recent results on alternating VASS.
In addition, we establish that the model-checking problem for RBTL is decidable and has the same complexity as for RBTL* (the extension of RBTL with arbitrary path formulae), namely EXPSPACE-complete, proving a new decidability result as a by-product of the approach. Finally, we establish that the model-checking problem for RB+-ATL* is decidable by a reduction to parity games, and show how to synthesise values for resource parameters
Regular Separability of Well-Structured Transition Systems
We investigate the languages recognized by well-structured transition systems (WSTS) with upward and downward compatibility. Our first result shows that, under very mild assumptions, every two disjoint WSTS languages are regular separable: There is a regular language containing one of them and being disjoint from the other. As a consequence, if a language as well as its complement are both recognized by WSTS, then they are necessarily regular. In particular, no subclass of WSTS languages beyond the regular languages is closed under complement. Our second result shows that for Petri nets, the complexity of the backwards coverability algorithm yields a bound on the size of the regular separator. We complement it by a lower bound construction
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