# Patrick TotzkeUniversity of Liverpool | UoL · Department of Computer Science

Patrick Totzke

PhD

## About

41

Publications

1,081

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

193

Citations

Citations since 2016

Introduction

Hey there! I am a theoretical computer scientist by day, based in sunny Liverpool where I am a member of the Verification Group.
I am interested in all things logics, automata, game theory and computer-aided verification. Most of my published work is on infinite-state models and includes extensions of vector addition systems with data, pushdown stack, alternation or branching. These days, I mostly focus on timed automata and (stochastic) games played on graphs.

Additional affiliations

January 2015 - January 2016

April 2014 - February 2015

October 2010 - April 2014

## Publications

Publications (41)

An automaton is history-deterministic (HD) if one can safely resolve its non-deterministic choices on the fly. In a recent paper, Henzinger, Lehtinen and Totzke studied this in the context of Timed Automata [9], where it was conjectured that the class of timed \(\omega \)-languages recognised by HD-timed automata strictly extends that of determinis...

We study countably infinite stochastic 2-player games with reachability objectives. Our results provide a complete picture of the memory requirements of $\varepsilon$-optimal (resp. optimal) strategies. These results depend on whether the game graph is infinitely branching and on whether one requires strategies that are uniform (i.e., independent o...

Temporal logics for the specification of information-flow properties are able to express relations between multiple executions of a system. The two most important such logics are HyperLTL and HyperCTL*, which generalise LTL and CTL* by trace quantification. It is known that this expressiveness comes at a price, i.e. satisfiability is undecidable fo...

We study stochastic games with energy-parity objectives, which combine quantitative rewards with a qualitative ω-regular condition: The maximizer aims to avoid running out of energy while simultaneously satisfying a parity condition. We show that the corresponding almost-sure problem, i.e., checking whether there exists a maximizer strategy that ac...

We study stochastic games with energy-parity objectives, which combine quantitative rewards with a qualitative $\omega$-regular condition: The maximizer aims to avoid running out of energy while simultaneously satisfying a parity condition. We show that the corresponding almost-sure problem, i.e., checking whether there exists a maximizer strategy...

Chapter ‘Recent Advances on Reachability Problems for Valence Systems’ is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

The Transient objective is not to visit any state infinitely often. While this is not possible in any finite Markov Decision Process (MDP), it can be satisfied in countably infinite ones, e.g., if the transition graph is acyclic. We prove the following fundamental properties of Transient in countably infinite MDPs. 1. There exist uniformly $\epsilo...

We study countably infinite MDPs with parity objectives. Unlike in finite MDPs, optimal strategies need not exist, and may require infinite memory if they do. We provide a complete picture of the exact strategy complexity of $\varepsilon$-optimal strategies (and optimal strategies, where they exist) for all subclasses of parity objectives in the Mo...

We study the language universality problem for One-Counter Nets, also known as 1-dimensional Vector Addition Systems with States (1-VASS), parameterized either with an initial counter value, or with an upper bound on the allowed counter value during runs. The language accepted by an OCN (defined by reaching a final control state) is monotone in bot...

Infinite-duration games with disturbances extend the classical framework of infinite-duration games, which captures the reactive synthesis problem, with a discrete measure of resilience against non-antagonistic disturbances, i.e., unmodeled situations in which the actual controller action differs from the intended one. For games played on finite ar...

Bertrand et al. [1] (LMCS 2019) describe two-player zero-sum games in which one player tries to achieve a reachability objective in $n$ games (on the same finite arena) simultaneously by broadcasting actions, and where the opponent has full control of resolving non-deterministic choices. They show EXPTIME completeness for the question if such games...

Timed basic parallel processes (TBPP) extend communication-free Petri nets (aka. BPP or commutative context-free grammars) by a global notion of time. TBPP can be seen as an extension of timed automata (TA) with context-free branching rules, and as such may be used to model networks of independent timed automata with process creation. We show that...

We study countably infinite Markov decision processes with B\"uchi objectives, which ask to visit a given subset of states infinitely often. A question left open by T.P. Hill in 1979 is whether there always exist $\varepsilon$-optimal Markov strategies, i.e., strategies that base decisions only on the current state and the number of steps taken so...

A timed network consists of an arbitrary number of initially identical 1-clock timed automata, interacting via hand-shake communication. In this setting there is no unique central controller, since all automata are initially identical. We consider the universal safety problem for such controller-less timed networks, i.e., verifying that a bad event...

We show how the yardstick construction of Stockmeyer, also developed as counter bootstrapping by Lipton, can be adapted and extended to obtain new lower bounds for the coverability problem for two prominent classes of systems based on Petri nets: Ackermann-hardness for unordered data Petri nets, and Tower-hardness for pushdown vector addition syste...

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...

Energy-parity objectives combine $\omega$-regular with quantitative objectives of reward MDPs. The controller needs to avoid to run out of energy while satisfying a parity objective. We refute the common belief that, if an energy-parity objective holds almost-surely, then this can be realised by some finite memory strategy. We provide a surprisingl...

We show how the yardstick construction of Stockmeyer, also developed as counter bootstrapping by Lipton, can be adapted and extended to obtain new lower bounds for the coverability problem for two prominent classes of systems based on Petri nets: Ackermann-hardness for unordered data Petri nets, and Tower-hardness for pushdown vector addition syste...

Data vectors generalise finite multisets: they are finitely supported functions into a commutative monoid. We study the question if 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. Based on a succinct represe...

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 qu...

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 ho...

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 p...

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.

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 qu...

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 p...

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 bounded...

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 decidabili...

We study the decidability and complexity of verification problems for infinite-state systems.
A fundamental question in formal verification is if the behaviour of one process is reproducible
by another. This inclusion problem can be studied for various models of computation
and behavioural preorders. It is generally intractable or even undecidable...

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...

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 f...

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...

We consider the model checking problem for Gap-order Constraint Systems (GCS)
w.r.t. the branching-time temporal logic CTL, and in particular its fragments
EG and EF.
GCS are nondeterministic infinitely branching processes described by
evolutions of integer-valued variables, subject to Presburger constraints of
the form $x-y\ge k$, where $x$ and $y...

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 omega, but only at omega^2. In
contrast, other semantic relations...

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...

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

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...

We investigate the (non)-existence of universal automata for var-ious classes of automata, as finite and pushdown automata, and in particular the influence of the representation and encoding function. An alternative approach, using transition systems, is presented too.

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

Two kinds of multiset automata with a storage attached, varying only in their ability of testing the storage for emptiness, are introduced, as well as normal forms. Their accepting power and relation to other multiset languages classes is investigated.

## Projects

Projects (3)