Related papers: Cons-free Programs and Complexity Classes between …
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
We investigate the minimum cases for realtime probabilistic machines that can define uncountably many languages with bounded error. We show that logarithmic space is enough for realtime PTMs on unary languages. On binary case, we follow the…
In this paper we obtain complexity bounds for computational problems on algebraic power series over several commuting variables. The power series are specified by systems of polynomial equations: a formalism closely related to weighted…
We prove that QCSP$(\mathbb{N};x=y\rightarrow y=z)$ is PSpace-complete, settling a question open for more than ten years. This completes the complexity classification for the QCSP over equality languages as a trichotomy between Logspace,…
The Lorentz lattice gas is studied from the perspective of computational complexity theory. It is shown that using massive parallelism, particle trajectories can be simulated in a time that scales logarithmically in the length of the…
These notes contain, among others, a proof that the average running time of an easy solution to the satisfiability problem for propositional calculus is, under some reasonable assumptions, linear (with constant 2) in the size of the input.…
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…
Log-likelihood vectors define a common space for comparing language models as probability distributions, enabling unified comparisons across heterogeneous settings. We extend this framework to training checkpoints and intermediate layers,…
Computing educators and researchers have used programming process data to understand how programs are constructed and what sorts of problems students struggle with. Although such data shows promise for using it for feedback, fully automated…
We investigate the power of non-determinism in purely functional programming languages with higher-order types. Specifically, we consider cons-free programs of varying data orders, equipped with explicit non-deterministic choice.…
Code reasoning tasks are becoming prevalent in large language model (LLM) assessments. Yet, there is a dearth of studies on the impact of real-world complexities on code reasoning, e.g., inter- or intra-procedural dependencies, API calls,…
Research at the intersection of machine learning, programming languages, and software engineering has recently taken important steps in proposing learnable probabilistic models of source code that exploit code's abundance of patterns. In…
We find polynomial-time solutions to the word problem for free-by-cyclic groups, the word problem for automorphism groups of free groups, and the membership problem for the handlebody subgroup of the mapping class group. All of these…
We consider well-known provability logic GLP. We prove that the GLP-provability problem for variable-free polymodal formulas is PSPACE-complete. For a number n, let L^n_0 denote the class of all polymodal variable-free formulas without…
Large Language Models (LLMs) like ChatGPT, Copilot, Gemini, and DeepSeek are transforming software engineering by automating key tasks, including code generation, testing, and debugging. As these models become integral to development…
To provide a dichotomy between those queries that can be made feasible on big data after appropriate preprocessing and those for which preprocessing does not help, Fan et al. developed the $\sqcap$-tractability theory. This theory provides…
We investigate the relationship between computation and spacetime structure, focussing on the role of closed timelike curves (CTCs) in promoting computational speedup. We note first that CTC traversal can be interpreted in two distinct…
If code is law, then the language of law is a programming language. Lawyers and legal scholars can learn about law by studying programming-language theory, and programming-language tools can be usefully applied to legal problems. This…
Integer linear programs $\min\{c^T x : A x = b, x \in \mathbb{Z}^n_{\ge 0}\}$, where $A \in \mathbb{Z}^{m \times n}$, $b \in \mathbb{Z}^m$, and $c \in \mathbb{Z}^n$, can be solved in pseudopolynomial time for any fixed number of constraints…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…