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- Piotr Hofman, Patrick Totzke
- RP
- 2014

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.… (More)

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… (More)

- Piotr Hofman, Slawomir Lasota, Ranko Lazic, Jérôme Leroux, Sylvain Schmitz, Patrick Totzke
- FoSSaCS
- 2016

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. We show how to… (More)

- Piotr Hofman, Richard Mayr, Patrick Totzke
- 2013 28th Annual ACM/IEEE Symposium on Logic in…
- 2013

One-counter nets 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 &omega;, but only at &omega;2. In contrast, other semantic relations like… (More)

- Piotr Hofman, Slawomir Lasota, Richard Mayr, Patrick Totzke
- FSTTCS
- 2013

General rights Copyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The University of Edinburgh has made every… (More)

- Jérôme Leroux, Grégoire Sutre, Patrick Totzke
- ICALP
- 2015

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… (More)

We study pushdown vector addition systems, which are synchronized products of pushdown automata with vector addition systems. The question of the boundedness of the reachability set for this model can be refined into two decision problems that ask if infinitely many counter values or stack configurations are reachable, respectively. Counter boundedness… (More)

- Manfred Kudlek, Patrick Totzke, Georg Zetzsche
- Fundam. Inform.
- 2009

- Matthias Englert, Ranko Lazic, Patrick Totzke
- LICS
- 2016

Blondin et al. showed at LICS 2015 that two-dimensional vector addition systems with states have reachability witnesses of length exponential in the number of states and polynomial in the norm of vectors. The resulting guess-and-verify algorithm is optimal (PSPACE), but only if the input vectors are given in binary. We answer positively the main question… (More)

- Piotr Hofman, Jérôme Leroux, Patrick Totzke
- 2017 32nd Annual ACM/IEEE Symposium on Logic in…
- 2017

Data vectors generalise finite multisets: they are finitely supported functions into a commutative monoid. We study the question whether a given data vector can be expressed as a finite sum of others, only assuming that 1) the domain is countable and 2) the given set of base vectors is finite up to permutations of the domain.