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Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
We consider the following natural graph cut problem called Critical Node Cut (CNC): Given a graph $G$ on $n$ vertices, and two positive integers $k$ and $x$, determine whether $G$ has a set of $k$ vertices whose removal leaves $G$ with at…
This paper describes a natural language parsing algorithm for unrestricted text which uses a probability-based scoring function to select the "best" parse of a sentence. The parser, Pearl, is a time-asynchronous bottom-up chart parser with…
We consider the computational complexity of pure Nash equilibria in graphical games. It is known that the problem is NP-complete in general, but tractable (i.e., in P) for special classes of graphs such as those with bounded treewidth. It…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
Temporal graphs are graphs whose edges are labelled with times at which they are active. Their time-sensitivity provides a useful model of real networks, but renders many problems studied on temporal graphs more computationally complex than…
We investigate the computational complexity of problems on toric ideals such as normal forms, Gr\"obner bases, and Graver bases. We show that all these problems are strongly NP-hard in the general case. Nonetheless, we can derive efficient…
Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…
Detecting and understanding reasons for defects and inadvertent behavior in software is challenging due to their increasing complexity. In configurable software systems, the combinatorics that arises from the multitude of features a user…
Conformal Prediction (CP) is a popular method for uncertainty quantification with machine learning models. While conformal prediction provides probabilistic guarantees regarding the coverage of the true label, these guarantees are agnostic…
We consider the reachability relation of pushdown systems whose pushdown holds a Mazurkiewicz trace instead of just a word as in classical systems. Under two natural conditions on the transition structure of such systems, we prove that the…
We consider the parameterised complexity of several list problems on graphs, with parameter treewidth or pathwidth. In particular, we show that List Edge Chromatic Number and List Total Chromatic Number are fixed parameter tractable,…
Machine Learning techniques have become pervasive across a range of different applications, and are now widely used in areas as disparate as recidivism prediction, consumer credit-risk analysis and insurance pricing. The prevalence of…
With recent advances in natural language processing, rationalization becomes an essential self-explaining diagram to disentangle the black box by selecting a subset of input texts to account for the major variation in prediction. Yet,…
Literature on Constraint Satisfaction exhibits the definition of several structural properties that can be possessed by CSPs, like (in)consistency, substitutability or interchangeability. Current tools for constraint solving typically…
Causal fairness in databases is crucial to preventing biased and inaccurate outcomes in downstream tasks. While most prior work assumes a known causal model, recent efforts relax this assumption by enforcing additional constraints. However,…
In many decision-making processes, one may prefer multiple solutions to a single solution, which allows us to choose an appropriate solution from the set of promising solutions that are found by algorithms. Given this, finding a set of…
We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…
In heap-based languages, knowing that a variable x points to an acyclic data structure is useful for analyzing termination: this information guarantees that the depth of the data structure to which x points is greater than the depth of the…
Many fundamental problems in artificial intelligence, knowledge representation, and verification involve reasoning about sets and relations between sets and can be modeled as set constraint satisfaction problems (set CSPs). Such problems…