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Filip Mazowiecki

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10 papers
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10

FOCS Conference 2024 Conference Paper

The Tractability Border of Reachability in Simple Vector Addition Systems with States

  • Dmitry Chistikov 0001
  • Wojciech Czerwinski
  • Filip Mazowiecki
  • Lukasz Orlikowski
  • Henry Sinclair-Banks
  • Karol Wegrzycki

Vector Addition Systems with States (VASS), equiv-alent to Petri nets, are a well-established model of concurrency. A d-VASS can be seen as directed graph whose edges are labelled by d-dimensional integer vectors. While following a path, the values of $d$ nonnegative integer counters are updated according to the integer labels. The central algorithmic challenge in VASS is the reachability problem: is there a run from a given starting node and counter values to a given target node and counter values? When the input is encoded in binary, reachability is computationally intractable: even in dimension one, it is NP-hard. In this paper, we comprehensively characterise the tractability border of the problem when the input is encoded in unary. For our main result, we prove that reachability is NP-hard in unary encoded 3-VASS, even when structure is heavily restricted to be a simple linear-path scheme. This improves upon a recent result of Czerwiński and Orlikowski [LICS 2022], in both the number of counters and expressiveness of the considered model, as well as answers open questions of Englert, Lazić, and Totzke [LICS 2016] and Leroux [PETRI NETS 2021]. The underlying graph structure of a simple linear path scheme (SLPS) is just a path with self-loops at each node. We also study the exceedingly weak model of computation that is SPLS with counter updates in { -1, 0, + 1 }. Here, we show that reachability is NP-hard when the dimension is bounded by O(a(k)), where $a$ is the inverse Ackermann function and $k$ bounds the size of the SLPS. We complement our result by presenting a polynomial-time algorithm that decides reachability in 2-SLPS when the initial and target configurations are specified in binary. To achieve this, we show that reachability in such instances is well-structured: all loops, except perhaps for a constant number, are taken either polynomially many times or almost maximally. This extends the main result of Englert, Lazić, and Totzke [LICS 2016] who showed the problem is in NL when the initial and target configurations are specified in unary.

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ICML Conference 2021 Conference Paper

Let's Agree to Degree: Comparing Graph Convolutional Networks in the Message-Passing Framework

  • Floris Geerts
  • Filip Mazowiecki
  • Guillermo A. Pérez

In this paper we cast neural networks defined on graphs as message-passing neural networks (MPNNs) to study the distinguishing power of different classes of such models. We are interested in when certain architectures are able to tell vertices apart based on the feature labels given as input with the graph. We consider two variants of MPNNS: anonymous MPNNs whose message functions depend only on the labels of vertices involved; and degree-aware MPNNs whose message functions can additionally use information regarding the degree of vertices. The former class covers popular graph neural network (GNN) formalisms for which the distinguished power is known. The latter covers graph convolutional networks (GCNs), introduced by Kipf and Welling, for which the distinguishing power was unknown. We obtain lower and upper bounds on the distinguishing power of (anonymous and degree-aware) MPNNs in terms of the distinguishing power of the Weisfeiler-Lehman (WL) algorithm. Our main results imply that (i) the distinguishing power of GCNs is bounded by the WL algorithm, but they may be one step ahead; (ii) the WL algorithm cannot be simulated by “plain vanilla” GCNs but the addition of a trade-off parameter between features of the vertex and those of its neighbours (as proposed by Kipf and Welling) resolves this problem.

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CSL Conference 2020 Conference Paper

A Robust Class of Linear Recurrence Sequences

  • Corentin Barloy
  • Nathanaël Fijalkow
  • Nathan Lhote
  • Filip Mazowiecki

We introduce a subclass of linear recurrence sequences which we call poly-rational sequences because they are denoted by rational expressions closed under sum and product. We show that this class is robust by giving several characterisations: polynomially ambiguous weighted automata, copyless cost-register automata, rational formal series, and linear recurrence sequences whose eigenvalues are roots of rational numbers.

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STOC Conference 2019 Conference Paper

The reachability problem for Petri nets is not elementary

  • Wojciech Czerwinski
  • Slawomir Lasota 0001
  • Ranko Lazic 0001
  • Jérôme Leroux
  • Filip Mazowiecki

Petri nets, also known as vector addition systems, are a long established model of concurrency with extensive applications in modelling and analysis of hardware, software and database systems, as well as chemical, biological and business processes. The central algorithmic problem for Petri nets is reachability: whether from the given initial configuration there exists a sequence of valid execution steps that reaches the given final configuration. The complexity of the problem has remained unsettled since the 1960s, and it is one of the most prominent open questions in the theory of verification. Decidability was proved by Mayr in his seminal STOC 1981 work, and the currently best published upper bound is non-primitive recursive Ackermannian of Leroux and Schmitz from LICS 2019. We establish a non-elementary lower bound, i.e. that the reachability problem needs a tower of exponentials of time and space. Until this work, the best lower bound has been exponential space, due to Lipton in 1976. The new lower bound is a major breakthrough for several reasons. Firstly, it shows that the reachability problem is much harder than the coverability (i.e., state reachability) problem, which is also ubiquitous but has been known to be complete for exponential space since the late 1970s. Secondly, it implies that a plethora of problems from formal languages, logic, concurrent systems, process calculi and other areas, that are known to admit reductions from the Petri nets reachability problem, are also not elementary. Thirdly, it makes obsolete the currently best lower bounds for the reachability problems for two key extensions of Petri nets: with branching and with a pushdown stack. At the heart of our proof is a novel gadget so called the factorial amplifier that, assuming availability of counters that are zero testable and bounded by k , guarantees to produce arbitrarily large pairs of values whose ratio is exactly the factorial of k . We also develop a novel construction that uses arbitrarily large pairs of values with ratio R to provide zero testable counters that are bounded by R . Repeatedly composing the factorial amplifier with itself by means of the construction then enables us to compute in linear time Petri nets that simulate Minsky machines whose counters are bounded by a tower of exponentials, which yields the non-elementary lower bound. By refining this scheme further, we in fact establish hardness for h -exponential space already for Petri nets with h + 13 counters.

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Highlights Conference 2018 Conference Abstract

Pumping lemmas for weighted automata

  • Filip Mazowiecki

ABSTRACT. We present three pumping lemmas for three classes of functions definable by fragments of weighted automata over the min-plus semiring and the semiring of natural numbers. As a corollary we show that the hierarchy of functions definable by unambiguous, finitely-ambiguous, polynomially-ambiguous weighted automata, and the full class of weighted automata is strict for the min-plus semiring. This is joint work with Cristian Riveros.

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Highlights Conference 2017 Conference Abstract

Timed pushdown automata and branching vector addition systems

  • Filip Mazowiecki

We prove that non-emptiness of timed register pushdown automata is decidable in doubly exponential time. This is a very expressive class of automata, whose transitions may involve state and top-of-stack clocks with unbounded differences. It strictly subsumes pushdown timed automata of Bouajjani et al. , dense-timed pushdown automata of Abdulla et al. , and orbit-finite timed register pushdown automata of Clemente and Lasota. Along the way, we prove two further decidability results of independent interest: for non-emptiness of least solutions to systems of equations over sets of integers with addition, union and intersections with natural numbers and their complement; and for reachability in one-dimensional branching vector addition systems with states and subtraction. Both are in exponential time.

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Highlights Conference 2015 Conference Abstract

Maximal partition logic: towards a logical characterization of copyless cost register automata

  • Filip Mazowiecki

It is desirable for a computational model to have a logic characterization like in the seminal work from Buchi that connects MSO with finite automata. For example, weighted automata are the quantitative extension of finite automata for computing functions over words and they can be naturally characterized by a fragment of weighted logic introduced by Droste and Gastin. Recently, cost register automata (CRA) were introduced by Alur et al. as an alternative model for weighted automata. In hope of finding decidable subclasses of weighted automata, they proposed to restrict their model with the so-called copyless restriction. Unfortunately, copyless CRA do not enjoy good closure properties and, therefore, a logical characterization of this class seems to be unlikely. We introduce a new logic called maximal partition logic (MP) for studying the expressiveness of copyless CRA. In contrast from the previous approaches (i. e. weighted logics), MP is based on a new set of regular quantifiers that partition a word into maximal subwords, compute the output of a subformula over each subword separately, and then aggregate these outputs with a semiring operation. We study the expressiveness of MP and compare it with weighted logics. Furthermore, we show that MP is equally expressive to a natural subclass of copyless CRA. This shows the first logical characterization of copyless CRA and it gives a better understanding of the copyless restriction in weighted automata. This is joint work with Cristian Riveros.

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CSL Conference 2015 Conference Paper

Maximal Partition Logic: Towards a Logical Characterization of Copyless Cost Register Automata

  • Filip Mazowiecki
  • Cristian Riveros

It is highly desirable for a computational model to have a logic characterization like in the seminal work from Buchi that connects MSO with finite automata. For example, weighted automata are the quantitative extension of finite automata for computing functions over words and they can be naturally characterized by a subframent of weighted logic introduced by Droste and Gastin. Recently, cost register automata (CRA) were introduced by Alur et al. as an alternative model for weighted automata. In hope of finding decidable subclasses of weighted automata, they proposed to restrict their model with the so-called copyless restriction. Unfortunately, copyless CRA do not enjoy good closure properties and, therefore, a logical characterization of this class seems to be unlikely. In this paper, we introduce a new logic called maximal partition logic (MPL) for studying the expressiveness of copyless CRA. In contrast from the previous approaches (i. e. weighted logics), MPL is based on a new set of "regular" quantifiers that partition a word into maximal subwords, compute the output of a subformula over each subword separately, and then aggregate these outputs with a semiring operation. We study the expressiveness of MPL and compare it with weighted logics. Furthermore, we show that MPL is equally expressive to a natural subclass of copyless CRA. This shows the first logical characterization of copyless CRA and it gives a better understanding of the copyless restriction in weighted automata.

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Highlights Conference 2014 Conference Abstract

Decidability of Weak Logics with Deterministic Transitive Closure

  • Filip Mazowiecki

The deterministic transitive closure operator, added to languages containing even only two variables, allows to express many natural properties of a binary relation, including being a linear order, a tree, a forest or a partial function. This makes it a potentially attractive ingredient of computer science formalisms. We consider the extension of the two-variable fragment of first-order logic by the deterministic transitive closure of a single binary relation, and prove that the satisfiability and finite satisfiability problems for the obtained logic are decidable and EXPSPACE-complete. This contrasts with the undecidability of two-variable logic with the deterministic transitive closures of several binary relations, known before. We also consider the class of universal first-order formulas in prenex form. Its various extensions by deterministic closure operations were earlier considered by other authors, leading to both decidability and undecidability results. We examine this scenario in more details. This is joint work with Witold Charatonik and Emanuel Kieroński.

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