University of Bremen - AlMoTh 2022https://www.uni-bremen.de/en/theorie/almoth-2022This is the homepage of the working group AGTI - "Theoretische Informatik" lead by Prof. Dr. Sebastian Siebertz.University of BremenThu, 08 Dec 2022 20:16:11 +0100Thu, 08 Dec 2022 20:16:11 +0100University of Bremenhttps://www.uni-bremen.de/en/theorie/almoth-2022#c416028Venue: Cartesium Enrique-Schmidt-Strasse, 28359 Bremen, Germany
Public transportation stop Streetcar: Universität-Süd Bus: Universität-Süd
Monday 21.3.
13:45 - 14:15 Erich Grädel: Zero-One Laws and Almost Sure Valuations of First-Order Logic in Semiring Semantics
14:15 - 14:45 Matthias Naaf: Fixed-Point Logic with Semiring Semantics: How to Compute Greatest Fixed Points
14:45 - 15:15 Florian Bruse: A Decidable Non-Regular Modal Fixpoint Logic
15:15 - 15:45 Coffee Break
15:45 - 16:15 Sarah Kleest-Meißner: Discovering Event Queries from Traces: Laying Foundations for Subsequence-Queries with Wildcards and Gap-Size Constraints
16:15 - 16:45 Max Merz: Probabilistic Databases under Updates: Boolean Query Evaluation and Ranked Enumeration
16:45 - 17:00 Short Break
17:00 - 17:30 Christoph Standke: Probabilistic Query Evaluation with Bag Semantics
17:30 - 18:00 Alexandre Vigny: Discrepancy and Sparsity
Tuesday
9:00 - 9:30 Benedikt Pago: Distinguishing graphs in Choiceless Polynomial Time and the Extended Polynomial Calculus.
9:30 - 10:00 Moritz Lichter: Extending Choiceless Polynomial Time with Choices
10:00 - 10:30 Nicole Schirrmacher: Separator logic and disjoint-paths logic
10:30 - 11:00 Coffee Break
11:00 - 11:30 Nikolas Mählmann: Indiscernible sequences in monadically stable and monadically NIP classes
11:30 - 12:00 Marko Schmellenkamp: Iltis: Learning Logic in the Web
12:00 - 12:30 Tim Seppelt. Homomorphism Tensors and Linear Equations
Hotel recommendations near Campus
7THINGS - my basic hotel Atlantic Hotels Bremen Hotel Munte am Stadtwald
Participants
Martin Grohe Erich Grädel Amer E. Mouawad Sebastian Siebertz Bartosz Bednarczyk Nikolas Mählmann Dietrich Kuske Manuel Bodirsky Nicole Schirrmacher Sarah Kleest-Meißner Benedikt Pago Sandra Kiefer Matthias Naaf Kord Eickmeyer Carsten Lutz Christoph Berkholz Marko Schmellenkamp Fabian Vehlken Marius Tritschler Felix Tschirbs Eva Fluck Tim Seppelt Steffen van Bergerem Christoph Standke Timo Gervens Louis Härtel Hinrikus Wolf Martin Otto Žaneta Semanišinová Clotilde Bizière Christopher Hugenroth Moritz Lichter Jonas Schmidt Benjamin Scheidt Jennifer Todtenhoefer Marcelo Garlet Milani Meike Hatzel Max Merz Florian Bruse Harry Vinall-Smeeth Maurice Funk Maximilian Gorsky Stephan KreutzerContentcontent-416028Wed, 16 Mar 22 15:29:24 +0100Sarah Kleest-Meißner https://www.uni-bremen.de/en/theorie/almoth-2022#c416020Discovering Event Queries from Traces: Laying Foundations for Subsequence-Queries with Wildcards and Gap-Size Constraints
We introduce subsequence-queries with wildcards and gap-size constraints (swg-queries, for short) as a tool for querying event traces. An swg-query q is given by a string s over an alphabet of variables and types, a global window size w and a tuple c = ((c_1^-,c_1^+),(c_2^-,c_2^+), ..., (c_(|s|-1)^-, c_(|s|-1)^+)) of local gap-size constraints. The query q matches in a trace t (i.e., a sequence of types) if the variables can uniformly be substituted by types such that the resulting string occurs in t as a subsequence that spans an area of length at most w, and the i-th gap of the subsequence (i. e., the distance between the i-th and (i+1)-th position of the subsequence) has length at least c_i^- and at most c_i+. We formalise and investigate the task of discovering an swg-query that describes best the traces from a given sample S of traces, and we present an algorithm solving this task. As a central component, our algorithm repeatedly solves the matching problem (i.e., deciding whether a given query q matches in a given trace t), which is an NP-complete problem (in combined complexity). Hence, the matching problem is of special interest in the context of query discovery, and we therefore subject it to a detailed (parameterised) complexity analysis to identify tractable subclasses, which lead to tractable subclasses of the discovery problem as well. We complement this by a reduction proving that any query discovery algorithm also yields an algorithm for the matching problem. Hence, lower bounds on the complexity of the matching problem directly translate into according lower bounds of the query discovery problem.Contentcontent-416020Fri, 18 Feb 22 11:56:06 +0100Benedikt Pagohttps://www.uni-bremen.de/en/theorie/almoth-2022#c416021Distinguishing graphs in Choiceless Polynomial Time and the Extended Polynomial Calculus.
We extend prior work on the connections between logics from finite model theory and propositional/algebraic proof systems. We show that if all non-isomorphic graphs in a given graph class can be distinguished in the logic Choiceless Polynomial Time with counting (CPT), then they can also be distinguished in the bounded-degree extended polynomial calculus (EPC), and the refutations have roughly the same size as the resource consumption of the CPT-sentence. This allows to transfer lower bounds for EPC to CPT and thus constitutes a new potential approach towards understanding the limits of CPT. A super-polynomial EPC lower bound for a PTIME-instance of the graph isomorphism problem would separate CPT from P and thus solve a major open question in finite model theory. Further, our result yields a model theoretic proof for the separation of the bounded-degree polynomial calculus from the bounded-degree extended polynomial calculus.Contentcontent-416021Fri, 18 Feb 22 11:55:27 +0100Matthias Naafhttps://www.uni-bremen.de/en/theorie/almoth-2022#c416138Fixed-Point Logic with Semiring Semantics: How to Compute Greatest Fixed Points
We discuss the algorithmic evaluation of formulae in least fixed-point logic LFP under semiring semantics, which generalises Boolean semantics by replacing truth values with values from a commutative semiring. These values can represent information such as confidence or costs, and can also be used for provenance analysis of games with fixed-point objectives, such as Büchi games. The evaluation of LFP-formulae (in a given structure with semiring annotations) then requires the computation of fixed points over semirings, which is non-trivial for infinite semirings. We show that in absorptive semirings (with certain completeness assumptions), both least and greatest fixed points of polynomial systems, such as the ones induced by LFP-formulae, can be computed in a polynomial number of semiring operations.Contentcontent-416138Fri, 18 Feb 22 11:54:49 +0100 Tim Seppelthttps://www.uni-bremen.de/en/theorie/almoth-2022#c417024Homomorphism Tensors and Linear Equations
Lovász (1967) showed that two graphs $G$ and $H$ are isomorphic if and only if they are homomorphism indistinguishable over the class of all graphs, i.e. for every graph $F$, the number of homomorphisms from $F$ to $G$ equals the number of homomorphisms from $F$ to $H$. Recently, homomorphism indistinguishability over restricted classes of graphs such as bounded treewidth, bounded treedepth and planar graphs, has emerged as a surprisingly powerful framework for capturing diverse equivalence relations on graphs arising from logical equivalence and algebraic equation systems.
In this talk, a unified algebraic framework for such results is introduced by examining the linear-algebraic and representation-theoretic structure of tensors counting homomorphisms from labelled graphs. The existence of certain linear transformations between such homomorphism tensor subspaces can be interpreted both as homomorphism indistinguishability over a graph class and as feasibility of an equational system.
This is joint work with Martin Grohe and Gaurav Rattan.Contentcontent-417024Fri, 18 Feb 22 11:53:52 +0100Erich Grädelhttps://www.uni-bremen.de/en/theorie/almoth-2022#c417628Zero-One Laws and Almost Sure Valuations of First-Order Logic in Semiring Semantics
Semiring semantics evaluates logical statements not just to true or false, but to values in some commutative semiring.
As part of a general project to study the (finite) model theory of semiring semantics, we consider here random semiring interpretations, induced by a probability distribution on a (finite or infinite) semiring, and we investigate here the question of how classical results on first-order logic on random structures, most importantly the 0-1 law, generalise to semiring semantics.
It is an immediate consequence of the classical 0-1 law that a first-order sentence is, asymptotically, either almost surely evaluated to 0 by random semiring interpretations, or almost surely takes only values different from 0. However, by means of a more sophisticated analysis, based on appropriate extension properties and on algebraic representations of first-order formulae by polynomials, we can prove stronger results.
For many semirings, FO can be partitioned into classes F(j), such that every sentence in F(j) evaluates almost surely to j under random semiring interpretations. Further, for most of the semirings studied here, this partition actually collapses to just three classes F(0), F(1), and F(e), of sentences that, respectively, almost surely evaluate to 0, 1, and to the infimum e of all non-zero values of the semiring. For all other values j in the semiring we have that F(j) is empty.
A semiring where the analysis is somewhat different is the natural semiring (N,+,*,0,1) for which multiplication is increasing rather than decreasing with respect to the natural semiring order.
This is joint work with Hayyan Helal, Matthias Naaf, and Richard Wilke. Contentcontent-417628Wed, 23 Feb 22 13:31:05 +0100Moritz Lichterhttps://www.uni-bremen.de/en/theorie/almoth-2022#c420172Extending Choiceless Polynomial Time with Choices
Choiceless Polynomial Time (CPT) is the currently only remaining promising candidate in the quest for a logic capturing PTime. We extend CPT with a choice operator allowing choices from definable orbits. To ensure polynomial time evaluation, automorphisms have to be provided to certify that the choice set is indeed an orbit.
For the resulting logic we show that for every class of structures for which isomorphism is definable, the logic automatically captures PTime. To do so we argue that, in this logic, definable isomorphism implies definable canonization.
Thereby, our construction removes the non-trivial step of extending isomorphism definability results to canonization. This step was a part of proofs that show that CPT or other logics capture PTime on a particular class of structures. The step typically required substantial extra effort.Contentcontent-420172Wed, 02 Mar 22 13:02:19 +0100Max Merzhttps://www.uni-bremen.de/en/theorie/almoth-2022#c421747Probabilistic Databases under Updates: Boolean Query Evaluation and Ranked Enumeration
This talk will be about query evaluation on tuple-independent probabilistic databases in a dynamic setting, where tuples can be inserted or deleted. In this context we are interested in efficient data structures for maintaining the query result of Boolean as well as non-Boolean queries. For Boolean queries, we show how the known lifted inference rules can be made dynamic, so that they support single-tuple updates with only a constant number of arithmetic operations. As a consequence, we obtain that the probability of every safe UCQ can be maintained with constant update time. For non-Boolean queries, our task is to enumerate all result tuples ranked by their probability. We develop lifted inference rules for non-Boolean queries, and, based on these rules, provide a dynamic data structure that allows both log-time updates and ranked enumeration with logarithmic delay. As an application, we identify a fragment of non-repeating conjunctive queries that supports log-time updates as well as log-delay ranked enumeration. This characterisation is tight under the OMv-conjecture. This is joint work with Christoph Berkholz.
Contentcontent-421747Thu, 10 Mar 22 13:36:41 +0100Florian Brusehttps://www.uni-bremen.de/en/theorie/almoth-2022#c421748A Decidable Non-Regular Modal Fixpoint Logic
Fixpoint Logic with Chop (FLC) extends the modal $\mu$-calculus with an operator for sequential composition between predicate transformers. This makes it an expressive modal fixpoint logic which is capable of formalising many non-regular program properties. Its satisfiability problem is highly undecidable. Here we define Visibly Pushdown Fixpoint Logic with Chop (vpFLC), a fragment in which fixpoint formulas are required to be of a certain form resembling visibly pushdown grammars. We give a sound and complete game-theoretic characterisation of FLC's satisfiability problem and show that the games corresponding to formulas from vpFLC are stair-parity games and therefore effectively solvable, resulting in 2-EXPTIME-completeness of this fragment. The lower bound is inherited from PDL over Recursive Programs, which is structurally similar but considerably weaker in expressive power. This is joint work with Martin Lange.Contentcontent-421748Thu, 10 Mar 22 13:36:43 +0100Nicole Schirrmacherhttps://www.uni-bremen.de/en/theorie/almoth-2022#c422432Separator logic and disjoint-paths logic
Separator logic FO+conn and disjoint-paths logic FO+DP are extensions of first-order logic FO by connectivity predicates conn_k and disjoint-paths predicates disjoint-paths_k. We study the expressive power of these logics and their model-checking problem. Separator logic can express e.g. acyclicity, k-connectivity, and elimination distance problems to first-order definition classes. Its model-checking problem is fixed-parameter tractable on classes of graphs with excluded topological minor. Disjoint-paths logic can additionally express e.g. the disjoint-paths problem, the existence of (topological) minor, and planarity. This is joint work with Sebastian Siebertz and Alexandre Vigny.Contentcontent-422432Mon, 14 Mar 22 09:58:23 +0100Marko Schmellenkamphttps://www.uni-bremen.de/en/theorie/almoth-2022#c422642Iltis: Learning Logic in the Web
The Iltis project provides an interactive, web-based system for teaching the foundations of formal methods. It is designed with the objective to allow for simple inclusion of new educational tasks; to pipeline such tasks into more complex exercises; and to allow simple inclusion and cascading of feedback mechanisms. Currently, exercises for many typical automated reasoning workflows for propositional logic, modal logic, and some parts of first-order logic are covered. In this talk I will address (algorithmic) challenges and solution approaches for building such systems, but also show how the system can be used in logic instruction.Contentcontent-422642Mon, 14 Mar 22 12:59:06 +0100 Alexandre Vignyhttps://www.uni-bremen.de/en/theorie/almoth-2022#c422643Discrepancy and Sparsity
Discrepancy is a measure of the intricacy of a set system. A prime example of a set system are families of sets that are definable in a graph (using e.g. FO formulas). For example, the family of all neighborhoods, or all 2-hop neighborhoods. We show strong connections between the discrepancy of definable set systems and sparsity notions of graph classes such as: bounded degeneracy, bounded expansion, and nowhere dense. These results where obtained in collaboration with Mario Grobler, Yiting Jiang, Patrice Ossona de Mendez, and Sebastian Siebertz.Contentcontent-422643Mon, 14 Mar 22 12:59:07 +0100Nikolas Mählmannhttps://www.uni-bremen.de/en/theorie/almoth-2022#c422847Indiscernible sequences in monadically stable and monadically NIP classes
An indiscernible sequence in a structure is a sequence of elements which is very homogeneous in the sense that any two finite sub-sequences of the same length satisfy the same first-order formulas. We provide new characterizations of monadically stable and monadically NIP classes of structures in terms of indiscernible sequences by showing that they impose a strongstructure on their neighborhoods. From their study we derive several interesting combinatorial and algorithmic properties of monadically stable classes of finite graphs.Contentcontent-422847Tue, 15 Mar 22 07:46:29 +0100 Christoph Standkehttps://www.uni-bremen.de/en/theorie/almoth-2022#c422848Probabilistic Query Evaluation with Bag Semantics
Probabilistic databases (PDBs) are usually introduced as probability spaces over the subsets of a finite set of possible facts. Probabilistic query evaluation (PQE) is the problem of finding the probability that a Boolean query evaluates to true on a given PDB. The data complexity of PQE is well-understood for the classof unions of conjunctive queries on tuple-independent PDBs: for every query, the problem can be classified to be either solvable in polynomial time, or is #P-hard (Dalvi & Suciu, JACM 2012). In this talk, we discuss a version of PQE, where both the query evaluation, and the probabilistic databases use a bag semantics. That is, the input PDB may contain duplicates, and the query evaluation takes tuple multiplicities into account. Our main focus lies on self-join free conjunctive queries, where we obtain a dichotomy similar to the one above. This is achieved by combining known results for the set version of the problem with novel techniques that are required to handle distributions over multiplicities. This is joint work with Martin Grohe and Christoph Standke.Contentcontent-422848Tue, 15 Mar 22 07:46:30 +0100AlMoTh 2022https://www.uni-bremen.de/en/theorie/almoth-2022#c414871The AlMoTh 2022 meeting will take place in Bremen, on Monday/Tuesday, March 21rst and 22nd.
For registration please send an email to almoth[at]uni-bremen[dot]de If you are interested to give a talk, please add title and abstract.
Programm
Monday 12:00-13:30 Welcome Soup 13:30-18:00 Presentations 19:30 Dinner
Tuesday 9:00-13:00 PresentationsContentcontent-414871Tue, 15 Mar 22 10:59:01 +010060