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- research-articleJuly 2024
The Finite Satisfiability Problem for PCTL is Undecidable
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 22, Pages 1–14https://doi.org/10.1145/3661814.3662145We show that the problem of whether a given PCTL formula has a finite model is undecidable. The undecidability result holds even for formulae of the form [EQUATION] where the validity of ϕ1, ϕ2 depends only on the states reachable in at most two ...
- research-articleJuly 2024
A proof theory of right-linear (ω-)grammars via cyclic proofs
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 30, Pages 1–14https://doi.org/10.1145/3661814.3662138Right-linear (or left-linear) grammars are a well-known class of context-free grammars computing just the regular languages. They may naturally be written as expressions with least fixed points but with products restricted to letters as left arguments, ...
- research-articleJuly 2024
Primitive Recursive Dependent Type Theory
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 18, Pages 1–12https://doi.org/10.1145/3661814.3662136We show that restricting the elimination principle of the natural numbers type in Martin-Löf Type Theory (MLTT) to a universe of types not containing ####II-types ensures that all definable functions are primitive recursive. This extends the concept of ...
- research-articleJuly 2024
Verifying Unboundedness via Amalgamation
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 4, Pages 1–15https://doi.org/10.1145/3661814.3662133Well-structured transition systems (WSTS) are an abstract family of systems that encompasses a vast landscape of infinite-state systems. By requiring a well-quasi-ordering (wqo) on the set of states, a WSTS enables generic algorithms for classic ...
- research-articleJuly 2024
Equivalence and Conditional Independence in Atomic Sheaf Logic
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 70, Pages 1–14https://doi.org/10.1145/3661814.3662132We propose a semantic foundation for logics for reasoning in settings that possess a distinction between equality of variables, a coarser equivalence of variables, and a notion of conditional independence between variables. We show that such relations ...
- research-articleJuly 2024
Element-free probability distributions and random partitions
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 12, Pages 1–14https://doi.org/10.1145/3661814.3662131An "element-free" probability distribution is what remains of a probability distribution after we forget the elements to which the probabilities were assigned. These objects naturally arise in Bayesian statistics, in situations where elements are used as ...
- research-articleJuly 2024
Natural numbers from integers
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 67, Pages 1–9https://doi.org/10.1145/3661814.3662129In homotopy type theory, a natural number type is freely generated by an element and an endomorphism. Similarly, an integer type is freely generated by an element and an automorphism. Using only dependent sums, identity types, extensional dependent ...
- research-articleJuly 2024
Relevant S is Undecidable
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 51, Pages 1–8https://doi.org/10.1145/3661814.3662128Since the introduction of the semilattice relevant logic S by [Urquhart 1972, 1973], its decision problem has persisted as an open problem.
[Urquhart 1984] showed that many relevant logics are undecidable, yet S eluded these techniques. Eventually, this ...
- research-articleJuly 2024
First order complexity of finite random structures
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 31, Pages 1–14https://doi.org/10.1145/3661814.3662127For a sequence of random structures with n-element domains over a relational signature, we define its FO complexity as a certain subset in the Banach space ℓ∞/c0. The well-known FO zero-one law and FO convergence law correspond to FO complexities equal ...
- research-articleJuly 2024
A Cartesian Closed Category for Random Variables
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 32, Pages 1–14https://doi.org/10.1145/3661814.3662126We present a novel, yet rather simple construction within the traditional framework of Scott domains to provide semantics to probabilistic programming, thus obtaining a solution to a long-standing open problem in this area. We work with the Scott domain ...
- research-articleJuly 2024
From Quantifier Depth to Quantifier Number: Separating Structures with k Variables
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 71, Pages 1–14https://doi.org/10.1145/3661814.3662125Given two n-element structures, A and ℬ, which can be distinguished by a sentence of k-variable first-order logic (ℒk), what is the minimum f(n) such that there is guaranteed to be a sentence Φ ∈ ℒk with at most f(n) quantifiers, such that A ⊨ Φ but ℬ ⊭ ...
- research-articleJuly 2024
Decidability and Complexity of Decision Problems for Affine Continuous VASS
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 7, Pages 1–13https://doi.org/10.1145/3661814.3662124Vector addition system with states (VASS) is a popular model for the verification of concurrent systems. VASS consists of finitely many control states and a set of counters which can be incremented and decremented, but not tested for zero. VASS is a ...
- research-articleJuly 2024
A Profunctorial Semantics for Quantum Supermaps
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 43, Pages 1–15https://doi.org/10.1145/3661814.3662123We identify morphisms of strong profunctors as a categorification of quantum supermaps. These black-box generalisations of diagrams-with-holes are hence placed within the broader field of profunctor optics, as morphisms in the category of copresheaves on ...
- research-articleJuly 2024
Bounding the Weisfeiler-Leman Dimension via a Depth Analysis of I/R-Trees
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 50, Pages 1–14https://doi.org/10.1145/3661814.3662122The Weisfeiler-Leman (WL) dimension is an established measure for the inherent descriptive complexity of graphs and relational structures. It corresponds to the number of variables that are needed and sufficient to define the object of interest in a ...
- research-articleJuly 2024
Complete Game Logic with Sabotage
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 1, Pages 1–15https://doi.org/10.1145/3661814.3662121Game logic with sabotage (GLs) is introduced as a simple and natural extension of Parikh's game logic with a single additional primitive, which allows players to lay traps for the opponent. GLs can be used to model infinite sabotage games, in which ...
- research-articleJuly 2024
Quantum advantage and CSP complexity
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 23, Pages 1–15https://doi.org/10.1145/3661814.3662118Information-processing tasks modelled by homomorphisms between relational structures can witness quantum advantage when entanglement is used as a computational resource. We prove that the occurrence of quantum advantage is determined by the same type of ...
- research-articleJuly 2024
First order distinguishability of sparse random graphs
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 44, Pages 1–14https://doi.org/10.1145/3661814.3662117We study the problem of distinguishing between two independent samples [EQUATION], [EQUATION] of a binomial random graph G(n, p) by first order (FO) sentences. Shelah and Spencer proved that, for a constant α ∈ (0, 1), G(n, n−-α) obeys FO zero-one law if ...
- research-articleJuly 2024
On the Separability Problem of VASS Reachability Languages
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 49, Pages 1–14https://doi.org/10.1145/3661814.3662116We show that the regular separability problem of VASS reachability languages is decidable and Fω-complete. At the heart of our decision procedure are doubly-marked graph transition sequences, a new proof object that tracks a suitable product of the VASS ...
- research-articleJuly 2024
On symmetries of spheres in univalent foundations
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 20, Pages 1–14https://doi.org/10.1145/3661814.3662115Working in univalent foundations, we investigate the symmetries of spheres, i.e., the types of the form ####Sn = ####Sn. The case of the circle has a slick answer: the symmetries of the circle form two copies of the circle. For higher-dimensional spheres,...
- research-articleJuly 2024
Uniformisation of Regular Relations in First-Order Logic with Two Variables
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 54, Pages 1–13https://doi.org/10.1145/3661814.3662114A uniformisation of a binary relation is a functional relation contained in it, with the same domain. The uniformisation problem asks whether such a uniformisation can be defined in a given formalism.
We solve this problem in the context of regular ...