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The central conjecture of parameterized complexity states that FPT is not equal to W[1], and is generally regarded as the parameterized counterpart to P != NP. We revisit the issue of the plausibility of FPT != W[1], focusing on two…
We initiate a program of parameterized proof complexity that aims to provide evidence that FPT is different from W[1]. A similar program already exists for the classes W[2] and W[SAT]. We contrast these programs and prove upper and lower…
Motivated by certain applications from physics, biochemistry, economics, and computer science, in which the objects under investigation are not accessible because of various limitations, we propose a trial-and-error model to examine…
We study two fundamental problems related to finding subgraphs: (1) given graphs G and H, Subgraph Test asks if H is isomorphic to a subgraph of G, (2) given graphs G, H, and an integer t, Packing asks if G contains t vertex-disjoint…
Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…
In this paper we propose a new approach for developing a proof that P=NP. We propose to use a polynomial-time reduction of a NP-complete problem to Linear Programming. Earlier such attempts used polynomial-time transformation which is a…
As probabilistic systems gain popularity and are coming into wider use, the need for a mechanism that explains the system's findings and recommendations becomes more critical. The system will also need a mechanism for ordering competing…
In the \probrFix problem, we are given a graph $G$, a (non-proper) vertex-coloring $c : V(G) \to [r]$, and a positive integer $k$. The goal is to decide whether a proper $r$-coloring $c'$ is obtainable from $c$ by recoloring at most $k$…
Twenty-seven years ago, E. Freuder highlighted that "Constraint programming represents one of the closest approaches computer science has yet made to the Holy Grail of programming: the user states the problem, the computer solves it".…
We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability,…
A polynomial Turing compression (PTC) for a parameterized problem $L$ is a polynomial time Turing machine that has access to an oracle for a problem $L'$ such that a polynomial in the input parameter bounds each query. Meanwhile, a…
In the talk at the workshop my aim was to demonstrate the usefulness of graph techniques for tackling problems that have been studied predominantly as problems on the term level: increasing sharing in functional programs, and addressing…
Rule-based models are attractive for various tasks because they inherently lead to interpretable and explainable decisions and can easily incorporate prior knowledge. However, such systems are difficult to apply to problems involving…
This article describes a Turing machine which can solve for $\beta^{'}$ which is RE-complete. RE-complete problems are proven to be undecidable by Turing's accepted proof on the Entscheidungsproblem. Thus, constructing a machine which…
Kernelization---a mathematical key concept for provably effective polynomial-time preprocessing of NP-hard problems---plays a central role in parameterized complexity and has triggered an extensive line of research. This is in part due to a…
The last decade has seen a revival of interest in pebble games in the context of proof complexity. Pebbling has proven a useful tool for studying resolution-based proof systems when comparing the strength of different subsystems, showing…
The usefulness of parameterized algorithmics has often depended on what Niedermeier has called, "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of…
The widespread application of pre-trained language models (PLMs) in natural language processing (NLP) has led to increasing concerns about their explainability. Selective rationalization is a self-explanatory framework that selects…
This article presents a technique for proving problems hard for classes of the polynomial hierarchy or for PSPACE. The rationale of this technique is that some problem restrictions are able to simulate existential or universal quantifiers.…
The constrained linear representability problem (CLRP) for polymatroids determines whether there exists a polymatroid that is linear over a specified field while satisfying a collection of constraints on the rank function. Using a computer…