32 accepted papers
Machine learning models now drive many critical decisions, making explanations of their reasoning essential. Recent work analyzes the complexity of exact explanations in transparent models, but these explanations are often too large for practical use. This has motivated research into probabilistic a
Streamlining constraints (or streamliners, for short) narrow the search space, enhancing the speed and feasibility of solving complex constraint satisfaction problems. Traditionally, streamliners were crafted manually or generated through systematically combined atomic constraints with high-effort o
List coloring extends graph coloring by assigning each vertex a list of allowed colors. A graph is k-choosable if it can be properly colored for any choice of lists with k colors each. Deciding k-choosability is π²ₚ-complete, bipartite graphs have unbounded list chromatic number, and planar graphs (
We consider the computational problem of compacting Tsetlin Machine (TM) classifiers by reducing the number of propositional clauses while preserving predictive accuracy. TMs trained with limited clause capacity often perform poorly because stochastic optimization cannot reliably find the few precis…
Graph generation and enumeration problems often require handling equivalent graphs---those that differ only in vertex labeling. We study how to extend SAT Modulo Symmetries (SMS), a framework for eliminating such redundant graphs, to handle more complex constraints. While SMS was originally designed…
We present a comprehensive classical and parameterized complexity analysis of decision tree pruning operations, extending recent research on the complexity of learning small decision trees. Thereby, we offer new insights into the computational challenges of decision tree simplification, a crucial as…
We develop a general algorithmic framework that allows us to obtain fixed-parameter tractability for computing smallest symbolic models that represent given data. Our framework applies to all ML model types that admit a certain extension property. By showing this extension property for decision tree…
Circuits in deterministic decomposable negation normal form (d-DNNF) are representations of Boolean functions that enable linear-time model counting. This paper strengthens our theoretical knowledge of what classes of functions can be efficiently transformed, or compiled, into d-DNNF. Our main cont…
Parity reasoning is challenging for Conflict-Driven Clause Learning (CDCL) SAT solvers. This has been observed even for simple formulas encoding two contradictory parity constraints with different variable orders (Chew and Heule 2020). We provide an analytical explanation for their hardness by showi…
We consider the NP-hard problem of finding a smallest decision tree representing a classification instance in terms of a partially defined Boolean function. Small decision trees are desirable to provide an interpretable model for the given data. We show that the problem is fixed-parameter tractable…
Causal discovery seeks to unveil causal relationships (represented as a so-called causal graph) from observational data. This paper investigates the complex relationship between the graph structure and the efficiency of constraint-based causal discovery algorithms. Our main contributions incl…
Solvers for propositional satisfiability (SAT) effectively tackle hard optimization problems. However, translating to SAT can cause a significant size increase, restricting its use to smaller instances. To mitigate this, frameworks using multiple local SAT calls for gradually improving a heuristic s…
This paper presents a rewriting method for Boolean circuits that minimizes small subcircuits with exact synthesis. Individual synthesis tasks are encoded as Quantified Boolean Formulas (QBFs) that capture the full flexibility for implementing multi-output subcircuits. This is in contrast to SAT-base…
We present a new SAT-based method for generating all graphs up to isomorphism that satisfy a given co-NP property. Our method extends the SAT Modulo Symmetry (SMS) framework with a technique that we call co-certificate learning. If SMS generates a candidate graph that violates the given co-NP prope…
The graph width-measure twin-width recently attracted great attention because of its solving power and generality. Many prominent NP-hard problems are tractable on graphs of bounded twin-width if a certificate for the twin-width bound is provided as an input. Bounded twin-width subsumes other promin…
Answer Set Programming (ASP) is a prominent modeling and solving framework. An inconsistent core (IC) of an ASP program is an inconsistent subset of rules. In the case of inconsistent programs, a smallest or subset-minimal IC contains crucial rules for the inconsistency. In this work, we study fndin…
One favors decision trees (DTs) of the smallest size or depth to facilitate explainability and interpretability. However, learning such an optimal DT from data is well-known to be NP-hard. To overcome this complexity barrier, Ordyniak and Szeider (AAAI 21) initiated the study of optimal DT learning…
Hypersphere classification is a classical and foundational method that can provide easy-to-process explanations for the classification of real-valued as well as binary data. However, obtaining an (ideally concise) explanation via hypersphere classification is much more difficult when dealing with bi…
We consider the computational problem of finding a smallest local explanation (anchor) for classifying a given feature vector (example) by a black-box model. After showing that the problem is NP-hard in general, we study various natural restrictions of the problem in terms of problem parameters to…
We propose a new score-based algorithm for learning the structure of a Bayesian Network (BN). It is the first algorithm that simultaneously supports the requirements of (i) learning a BN of bounded treewidth, (ii) satisfying expert constraints, including positive and negative ancestry properties bet…
Argumentation frameworks (AFs) are a core formalism in the field of formal argumentation. As most standard computational tasks regarding AFs are hard for the first or second level of the Polynomial Hierarchy, a variety of algorithmic approaches to achieve manageable runtimes have been considered in…
We introduce backdoor DNFs, as a tool to measure the theoretical hardness of CNF formulas. Like backdoor sets and backdoor trees, backdoor DNFs are defined relative to a tractable class of CNF formulas. Each conjunctive term of a backdoor DNF defines a partial assignment that moves the input CNF for…
Hypertree width is a prominent hypergraph invariant with many algorithmic applications in constraint satisfaction and databases. We propose a novel characterization for hypertree width in terms of linear elimination orderings. We utilize this characterization to generate a new SAT encodi…
A CNF formula is harder than another CNF formula with the same number of clauses if it requires a longer resolution proof. We introduce resolution hardness numbers; they give for m=1,2,... the length of a shortest proof of a hardest formula on m clauses. We compute the first ten resolution hardn…
We propose new methods for learning Bayesian networks (BNs) that reliably support fast inference. We utilize maximum state space size as a more fine-grained measure for the BN's reasoning complexity than the standard treewidth measure, thereby accommodating the possibility that variables range over…
We study the NP-hard problem of learning a decision tree (DT) of smallest depth or size from data. We provide the first parameterized complexity analysis of the problem and draw a detailed parameterized complexity map for the natural parameters: size or depth of the DT, maximum domain size of all fe…
Decision trees of low depth are beneficial for understanding and interpreting the data they represent. Unfortunately, finding a decision tree of lowest depth that correctly represents given data is NP-hard. Hence known algorithms either (i) utilize heuristics that do not optimize the depth or (ii)…
We study fundamental clustering problems for incomplete data. Specifically, given a set of incomplete d-dimensional vectors (representing rows of a matrix), the goal is to complete the missing vector entries in a way that admits a partitioning of the vectors into at most k clusters with radius or di…
We present a new approach for learning the structure of a treewidth-bounded Bayesian Network (BN). The key to our approach is applying an exact method (based on MaxSAT) locally, to improve the score of a heuristically computed BN. This approach allows us to scale the power of exact methods—so far on…
Treewidth and hypertree width have proven to be highly successful structural parameters in the context of the Constraint Satisfaction Problem (CSP). When either of these parameters is bounded by a constant, then CSP becomes solvable in polynomial time. However, here the order of the polynomial in th…
Cascading portfolio scheduling is a static algorithm selection strategy which uses a sample of test instances to compute an optimal ordering (a cascading schedule) of a portfolio of available algorithms. The algorithms are then applied to each future instance according to this cascading schedule, u…
We consider two matrix completion problems, in which we are given a matrix with missing entries and the task is to complete the matrix in a way that (1) minimizes the rank, or (2) minimizes the number of distinct rows. We study the parameterized complexity of the two aforementioned problems with res…