Related papers: Sublogarithmic uniform Boolean proof nets

We consider Proof Complexity in light of the unusual binary encoding of certain combinatorial principles. We contrast this Proof Complexity with the normal unary encoding in several refutation systems, based on Resolution and Integer Linear…

Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…

The analysis of concurrent and reactive systems is based to a large degree on various notions of process equivalence, ranging, on the so-called linear-time/branching-time spectrum, from fine-grained equivalences such as strong bisimilarity…

The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of…

The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof…

We study the computational complexity of the recently proposed nubot model of molecular-scale self-assembly. The model generalises asynchronous cellular automata to have non-local movement where large assemblies of molecules can be pushed…

Based on the recent development of commutator theory for loops, we provide both syntactic and semantic characterization of abelian normal subloops. We highlight the analogies between well known central extensions and central nilpotence on…

Random instances of feedforward Boolean circuits are studied both analytically and numerically. Evaluating these circuits is known to be a P-complete problem and thus, in the worst case, believed to be impossible to perform, even given a…

The rapid growth of the size and complexity in deep neural networks has sharply increased computational demands, challenging their efficient deployment in real-world scenarios. Boolean networks, constructed with logic gates, offer a…

We give an introduction to logic tailored for algebraists, explaining how proofs in linear logic can be viewed as algorithms for constructing morphisms in symmetric closed monoidal categories with additional structure. This is made explicit…

It is becoming increasingly important to understand the vulnerability of machine learning models to adversarial attacks. In this paper we study the feasibility of robust learning from the perspective of computational learning theory,…

We study the class $\textrm{AC}^0$ of functions computed by constant-depth polynomial-size arithmetic circuits of unbounded fan-in addition and multiplication gates. No model-theoretic characterization for arithmetic circuit classes is…

This paper presents a simple notion of proof net for multiplicative linear logic with units. Cut elimination is direct and strongly normalising, in contrast to previous approaches which resorted to moving jumps (attachments) of par units…

In this paper bounded model checking of asynchronous concurrent systems is introduced as a promising application area for answer set programming. As the model of asynchronous systems a generalisation of communicating automata, 1-safe Petri…

While on some natural distributions, neural-networks are trained efficiently using gradient-based algorithms, it is known that learning them is computationally hard in the worst-case. To separate hard from easy to learn distributions, we…

Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed…

Arithmetic circuits (AC) are circuits over the real numbers with 0/1-valued input variables whose gates compute the sum or the product of their inputs. Positive AC -- that is, AC representing non-negative functions -- subsume many…

Logic Programming languages and combinational circuit synthesis tools share a common "combinatorial search over logic formulae" background. This paper attempts to reconnect the two fields with a fresh look at Prolog encodings for the…

We present a proof of the algorithm for computing line bundle valued cohomology classes over toric varieties conjectured by R.~Blumenhagen, B.~Jurke and the authors (arXiv:1003.5217) and suggest a kind of Serre duality for combinatorial…

The circuit complexity class DLOGTIME-uniform AC^0 is known to be a modest subclass of DLOGTIME-uniform TC^0. The weakness of AC^0 is caused by the fact that AC^0 is not closed under restricting AC^0-computable queries into simple…