Patrick Totzke

Patrick Totzke
University of Liverpool | UoL · Department of Computer Science

PhD

About

41
Publications
1,081
Reads
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193
Citations
Citations since 2016
27 Research Items
158 Citations
2016201720182019202020212022051015202530
2016201720182019202020212022051015202530
2016201720182019202020212022051015202530
2016201720182019202020212022051015202530
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
The University of Warwick
Position
  • PostDoc Position
April 2014 - February 2015
Laboratoire Bordelais de Recherche en Informatique
Position
  • PostDoc Position
October 2010 - April 2014
The University of Edinburgh
Position
  • PhD Student

Publications

Publications (41)
Chapter
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...
Preprint
Full-text available
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...
Preprint
Full-text available
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...
Chapter
Full-text available
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...
Preprint
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...
Book
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.
Preprint
Full-text available
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...
Preprint
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...
Preprint
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...
Preprint
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...
Preprint
Full-text available
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...
Preprint
Full-text available
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...
Preprint
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...
Preprint
Full-text available
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...
Chapter
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...
Article
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...
Article
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...
Chapter
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...
Article
Full-text available
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...
Conference Paper
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...
Conference Paper
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...
Article
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...
Article
Full-text available
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.
Article
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...
Conference Paper
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...
Conference Paper
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...
Conference Paper
Full-text available
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...
Thesis
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...
Article
Full-text available
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...
Conference Paper
Full-text available
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...
Article
Full-text available
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...
Conference Paper
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
The previously introduced multiset language classes defined by multiset pushdown automata are being explored with respect to their closure properties and alternative characterizations.
Article
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...
Article
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.
Article
Full-text available
The previously introduced multiset language classes dened by multiset storage automata are being explored with respect to their closure properties and alternative characterizations.
Article
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.

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