Related papers: RCF2: Evaluation and Consistency

Given a first-order theory $T$ formulated in the usual language of first-order arithmetic, we say that $T$ is of *restricted complexity* if there is some natural number $n$ and some set $\mathcal A$ of $\Sigma_n$-sentences such that $T$ can…

We study preferential attachment (PA) trees with general attachment functions. PA suggests an intuitive monotonicity: if high-degree vertices are rewarded more strongly, then the resulting tree should become shallower. We examine this…

We propose $\omega$MSO$\Join$BAPA, an expressive logic for describing countable structures, which subsumes and transcends both Counting Monadic Second-Order Logic (CMSO) and Boolean Algebra with Presburger Arithmetic (BAPA). We show that…

We analyse how the standard reductions between constraint satisfaction problems affect their proof complexity. We show that, for the most studied propositional, algebraic, and semi-algebraic proof systems, the classical constructions of…

The past decade has witnessed substantial developments in string solving. Motivated by the complexity of string solving strategies adopted in existing string solvers, we investigate a simple and generic method for solving string…

We introduce a general framework for analyzing learning algorithms based on the notion of self-regularization, which captures implicit complexity control without requiring explicit regularization. This is motivated by previous observations…

We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…

Assuming $\rm PFA$, we shall use internally club $\omega_1$-guessing models as side conditions to show that for every tree $T$ of height $\omega_2$ without cofinal branches, there is a proper and $\aleph_2$-preserving forcing notion with…

This was supposed to be an appendix to the book "Non-structure", and probably will be if it materializes. It presents relevant material, sometimes new, which was used in works which were supposed to be part of that book. In section 1 we…

We initiate a systematic study of \emph{generic stability independence} and introduce the class of \emph{treeless theories} in which this notion of independence is particularly well-behaved. We show that the class of treeless theories…

I explore the relationships between Prawitz's approach to non-monotonic proof-theoretic validity, which I call reducibility semantics, and some later proof-theoretic approaches, which I call standard base semantics and Sandqvist's base…

We present a compositional framework for certifying resource bounds in typed programs. Terms are typed with synthesized bounds drawn from an abstract resource lattice, enabling uniform treatment of time, memory, gas, and domain-specific…

Large Language Models often improve accuracy on reasoning tasks by sampling multiple Chain-of-Thought (CoT) traces and aggregating them with majority voting (MV), a test-time technique called self-consistency. When we truncate a CoT partway…

A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…

In a constructive setting, no concrete formulation of ordinal numbers can simultaneously have all the properties one might be interested in; for example, being able to calculate limits of sequences is constructively incompatible with…

Ill-founded (or non-wellfounded) proof systems have emerged as a natural framework for inductive and coinductive reasoning. In such systems, soundness relies on global correctness criteria, such as the progressivity condition. Ensuring that…

We consider the problem of minimising the number of states in a multiplicity tree automaton over the field of rational numbers. We give a minimisation algorithm that runs in polynomial time assuming unit-cost arithmetic. We also show that a…

We establish an assume-guarantee (AG) framework for compositional reasoning about multi-objective queries in parametric probabilistic automata (pPA) - an extension to probabilistic automata (PA), where transition probabilities are functions…

We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…

We give a uniform construction that, on input of a recursive presentation $P$ of a group, outputs a recursive presentation of a torsion-free group, isomorphic to $P$ whenever $P$ is itself torsion-free. We use this to re-obtain a known…