Results 1 
8 of
8
Bisimilarity of onecounter processes is PSPACEcomplete
"... A onecounter automaton is a pushdown automaton over a singleton stack alphabet. We prove that the bisimilarity of processes generated by nondeterministic onecounter automata (with no εsteps) is in PSPACE. This improves the previously known decidability result (Jančar 2000), and matches the known ..."
Abstract

Cited by 12 (6 self)
 Add to MetaCart
A onecounter automaton is a pushdown automaton over a singleton stack alphabet. We prove that the bisimilarity of processes generated by nondeterministic onecounter automata (with no εsteps) is in PSPACE. This improves the previously known decidability result (Jančar 2000), and matches the known PSPACE lower bound (Srba 2009). We add the PTIMEcompleteness result for deciding regularity (i.e. finiteness up to bisimilarity) of onecounter processes.
Techniques for Decidability and Undecidability of Bisimilarity
, 1999
"... In this tutorial we describe general approaches to deciding bisimilarity between vertices of (infinite) directed edgelabelled graphs. The approaches are based on a systematic search following the definition of bisimilarity. We outline (in decreasing levels of detail) how the search is modified t ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
In this tutorial we describe general approaches to deciding bisimilarity between vertices of (infinite) directed edgelabelled graphs. The approaches are based on a systematic search following the definition of bisimilarity. We outline (in decreasing levels of detail) how the search is modified to solve the problem for finite graphs, BPP graphs, BPA graphs, normed PA graphs, and normed PDA graphs. We complete this by showing the technique used in the case of graphs generated by onecounter machines. Finally, we demonstrate a general reduction strategy for proving undecidability, which we apply in the case of graphs generated by stateextended BPP (a restricted form of labelled Petri nets).
Solving parity games on integer vectors
, 2013
"... Abstract. We consider parity games on infinite graphs where configurations are represented by controlstates and integer vectors. This framework subsumes two classic game problems: parity games on vector addition systems with states (VASS) and multidimensional energy parity games. We show that the m ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
(Show Context)
Abstract. We consider parity games on infinite graphs where configurations are represented by controlstates and integer vectors. This framework subsumes two classic game problems: parity games on vector addition systems with states (VASS) and multidimensional energy parity games. We show that the multidimensional energy parity game problem is interreducible with a subclass of singlesided parity games on VASS where just one player can modify the integer counters and the opponent can only change controlstates. Our main result is that the minimal elements of the upwardclosed winning set of these singlesided parity games on VASS are computable. This implies that the Pareto frontier of the minimal initial credit needed to win multidimensional energy parity games is also computable, solving an open question from the literature. Moreover, our main result implies the decidability of weak simulation preorder/equivalence between finitestate systems and VASS, and the decidability of model checking VASS with a large fragment of the modal µcalculus. 1
Recursive Petri Nets  Theory and Application to Discrete Event Systems
 ACTA INFORMATICA
"... In order to design and analyse complex systems, modelers need formal models with two contradictory requirements: a high expressivity and the decidability of behavioural property checking. Here we present and develop the theory of such a model, the recursive Petri nets. First, we show that the mechan ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
In order to design and analyse complex systems, modelers need formal models with two contradictory requirements: a high expressivity and the decidability of behavioural property checking. Here we present and develop the theory of such a model, the recursive Petri nets. First, we show that the mechanisms supported by recursive Petri nets enable to model patterns of discrete event systems related to the dynamic structure of processes. Furthermore, we prove that these patterns cannot be modelled by ordinary Petri nets. Then we study the decidability of some problems: reachability, finiteness and bisimulation. At last, we develop the concept of linear invariants for this kind of nets and we design efficient computations specifically tailored to take advantage of their structure.
On the ContextFreeness Problem for Vector Addition Systems
, 2013
"... Abstract—Petri nets, or equivalently vector addition systems (VAS), are widely recognized as a central model for concurrent systems. Many interesting properties are decidable for this class, such as boundedness, reachability, regularity, as well as contextfreeness, which is the focus of this paper. ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract—Petri nets, or equivalently vector addition systems (VAS), are widely recognized as a central model for concurrent systems. Many interesting properties are decidable for this class, such as boundedness, reachability, regularity, as well as contextfreeness, which is the focus of this paper. The contextfreeness problem asks whether the trace language of a given VAS is contextfree. This problem was shown to be decidable by Schwer in 1992, but the proof is very complex and intricate. The resulting decision procedure relies on five technical conditions over a customized coverability graph. These five conditions are shown to be necessary, but the proof that they are sufficient is only sketched. In this paper, we revisit the contextfreeness problem for VAS, and give a simpler proof of decidability. Our approach is based on witnesses of noncontextfreeness, that are bounded regular languages satisfying a nesting condition. As a corollary, we obtain that the trace language of a VAS is contextfree if, and only if, it has a contextfree intersection with every bounded regular language. KeywordsVector addition systems, Petri nets, contextfreeness, pushdown automata, bounded languages, semilinear sets. I.
Decidability of weak simulation on onecounter nets
 In Proc. of LICS 2013. IEEE
, 2013
"... Onecounter nets (OCN) are Petri nets with exactly one unbounded place. They are equivalent to a subclass of onecounter automata with only a weak test for zero. We show that weak simulation preorder is decidable for OCN and that weak simulation approximants do not converge at level ω, but only at ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Onecounter nets (OCN) are Petri nets with exactly one unbounded place. They are equivalent to a subclass of onecounter automata with only a weak test for zero. We show that weak simulation preorder is decidable for OCN and that weak simulation approximants do not converge at level ω, but only at ω2. In contrast, other semantic relations like weak bisimulation are undecidable for OCN [17], and so are weak (and strong) trace inclusion (Sec. 7). 1
Verifying chemical reaction network implementations: A pathway decomposition approach
 In VEMPD, Vienna Summer of Logic
, 2014
"... The emerging fields of genetic engineering, synthetic biology, DNA computing, DNA nanotechnology, and molecular programming herald the birth of a new information technology that acquires information by directly sensing molecules within a chemical environment, stores information in molecules such as ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
The emerging fields of genetic engineering, synthetic biology, DNA computing, DNA nanotechnology, and molecular programming herald the birth of a new information technology that acquires information by directly sensing molecules within a chemical environment, stores information in molecules such as DNA, RNA, and proteins, processes that information by means of chemical and biochemical transformations, and uses that information to direct the manipulation of matter at the nanometer scale. To scale up beyond current proofofprinciple demonstrations, new methods for managing the complexity of designed molecular systems will need to be developed. Here we focus on the challenge of verifying the correctness of molecular implementations of abstract chemical reaction networks, where operation in a wellmixed “soup ” of molecules is stochastic, asynchronous, concurrent, and often involves multiple intermediate steps in the implementation, parallel pathways, and side reactions. This problem relates to the verification of Petri Nets, but existing approaches are not sufficient for certain situations that commonly arise in molecular implementations, such as what we call “delayed choice. ” We formulate a new theory of pathway decomposition that provides an elegant formal basis for comparing chemical reaction network implementations, and we present an algorithm that computes this basis. We further show how pathway decomposition can be combined with weak bisimulation to handle a wider class that includes all currently known enzymefree DNA implementation techniques. We anticipate that our notion of logical equivalence between chemical reaction network implementations will be valuable for other molecular implementations such as biochemical enzyme systems, and perhaps even more broadly in concurrency theory.