Patrick Totzke

Coverability trees for petri nets with unordered data

We study an extension of classical Petri nets where tokens carry values from a countable data domain, that can be tested for equality upon firing transitions. These Unordered Data Petri Nets (UDPN) are well-structured and therefore allow generic decision procedures for several verification problems including coverability and boundedness.

Decidability of Weak Simulation on One-Counter Nets

One-counter nets (OCN) are Petri nets with exactly one unbounded place. They are equivalent to a subclass of one-counter 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 [1], and so are weak (and strong) trace inclusion (Sec. VII).

Properties of Multiset Language Classes Defined by Multiset Pushdown Automata

The previously introduced multiset language classes defined by multiset pushdown automata are being explored with respect to their closure properties and alternative characterizations.

Multiset Pushdown Automata

Multiset finite Automata, a model equivalent to regular commutative grammars, are extended with a multiset store and the accepting power of this extended model of computation is investigated. This type of multiset automata come in two flavours, varying only in the ability of testing the storage for emptiness. This paper establishes normal forms and relates the derived language classes to each other as well as to known multiset language classes.

SIMULATION PROBLEMS OVER ONE-COUNTER NETS

One-counter nets (OCN) are finite automata equipped with a counter that can store non-negative integer values, and that cannot be tested for zero. Equivalently, these are exactly 1-dimensional vector addition systems with states. We show that both strong and weak simulation preorder on OCN are PSPACE-complete.

On the Coverability Problem for Pushdown Vector Addition Systems in One Dimension

Does the trace language of a given vector addition system VAS intersect with a given context-free language? This question lies at the heart of several verification questions involving recursive programs with integer parameters. In particular, it is equivalent to the coverability problem for VAS that operate on a pushdown stack. We show decidability in dimension one, based on an analysis of a new model called grammar-controlled vector addition systems.

Infinite-state energy games

Energy games are a well-studied class of 2-player turn-based games on a finite graph where transitions are labeled with integer vectors which represent changes in a multidimensional resource (the energy). One player tries to keep the cumulative changes non-negative in every component while the other tries to frustrate this. We consider generalized energy games played on infinite game graphs induced by pushdown automata (modelling recursion) or their subclass of one-counter automata. Our main result is that energy games are decidable in the case where the game graph is induced by a one-counter automaton and the energy is one-dimensional. On the other hand, every further generalization is undecidable: Energy games on one-counter automata with a 2-dimensional energy are undecidable, and energy games on pushdown automata are undecidable even if the energy is one-dimensional. Furthermore, we show that energy games and simulation games are inter-reducible, and thus we additionally obtain several new (un)decidability results for the problem of checking simulation preorder between pushdown automata and vector addition systems.

Simulation Over One-counter Nets is PSPACE-Complete

One-counter nets (OCN) are Petri nets with exactly one unbounded place. They are equivalent to a subclass of one-counter automata with just a weak test for zero. Unlike many other semantic equivalences, strong and weak simulation preorder are decidable for OCN, but the computational complexity was an open problem. We show that both strong and weak simulation preorder on OCN are Pspace-complete.

Trace Inclusion for One-Counter Nets Revisited

One-counter nets (OCN) consist of a nondeterministic finite control and a single integer counter that cannot be fully tested for zero. They form a natural subclass of both One-Counter Automata, which allow zero-tests and Petri Nets/VASS, which allow multiple such weak counters. The trace inclusion problem has recently been shown to be undecidable for OCN. In this paper, we contrast the complexity of two natural restrictions which imply decidability.

Approximating Weak Bisimilarity of Basic Parallel Processes

This paper explores the well known approximation approach to decide weak bisimilarity of Basic Parallel Processes. We look into how different refinement functions can be used to prove weak bisimilarity decidable for certain subclasses. We also show their limitations for the general case. In particular, we show a lower bound of {\omega} \ast {\omega} for the approximants which allow weak steps and a lower bound of {\omega} + {\omega} for the approximants that allow sequences of actions. The former lower bound negatively answers the open question of Jan\v{c}ar and Hirshfeld.