Related papers: Proof Complexity of Symbolic QBF Reasoning

Signed systems were introduced as a general, syntax-independent framework for paraconsistent reasoning, that is, non-trivialised reasoning from inconsistent information. In this paper, we show how the family of corresponding paraconsistent…

A quantum circuit is a computational unit that transforms an input quantum state to an output one. A natural way to reason about its behavior is to compute explicitly the unitary matrix implemented by it. However, when the number of qubits…

Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…

With the rapid development of quantum computing, automatic verification of quantum circuits becomes more and more important. While several decision diagrams (DDs) have been introduced in quantum circuit simulation and verification, none of…

Solving non-linear Diophantine systems lies at the mathematical core of integer optimization and cryptography. While the general unbounded problem is undecidable, even over bounded integer domains it remains classically intractable in the…

We prove a general lower bound on the bounded-error entanglement-assisted quantum communication complexity of Boolean functions. The bound is based on the concept that any classical or quantum protocol to evaluate a function on distributed…

We consider Quantum OBDD model. It is restricted version of read-once Quantum Branching Programs, with respect to "width" complexity. It is known that maximal complexity gap between deterministic and quantum model is exponential. But there…

Background: Neuro-symbolic methods enhance the reliability of neural network classifiers through logical constraints, but they lack native support for ontologies. Objectives: We aim to develop a neuro-symbolic method that reliably outputs…

We present BAss (BDD-based ADF symbolic solver), a novel analysis tool for Abstract Dialectical Frameworks (ADFs) based on Binary Decision Diagrams (BDDs). It supports the fully symbolic computation of all admissible, complete, and…

Standard answer set programming (ASP) targets at solving search problems from the first level of the polynomial time hierarchy (PH). Tackling search problems beyond NP using ASP is less straightforward. The class of disjunctive logic…

We use the venerable "fooling set" method to prove new lower bounds on the quantum communication complexity of various functions. Let f:X x Y-->{0,1} be a Boolean function, fool^1(f) its maximal fooling set size among 1-inputs, Q_1^*(f) its…

The neural network has become an integral part of modern software systems. However, they still suffer from various problems, in particular, vulnerability to adversarial attacks. In this work, we present a novel program reasoning framework…

Proving proof-size lower bounds for $\mathbf{LK}$, the sequent calculus for classical propositional logic, remains a major open problem in proof complexity. We shed new light on this challenge by isolating the power of structural rules,…

Ontologies are used in various domains, with RDF and OWL being prominent standards for ontology development. RDF is favored for its simplicity and flexibility, while OWL enables detailed domain knowledge representation. However, as…

Chain reduction enables reduced ordered binary decision diagrams (BDDs) and zero-suppressed binary decision diagrams (ZDDs) to each take advantage of the others' ability to symbolically represent Boolean functions in compact form. For any…

In this paper, we develop a way to encode several NP-Complete problems in Abstract Argumentation to Quadratic Unconstrained Binary Optimization (QUBO) problems. In this form, a solution for a QUBO problem involves minimizing a quadratic…

In computational argumentation, gradual semantics are fine-grained alternatives to extension-based and labelling-based semantics . They ascribe a dialectical strength to (components of) arguments sanctioning their degree of acceptability.…

Traditional Turing machines are semantically poor, they only concern the syntactic manipulation of symbols, discarding the mathematical semantics behind the symbols. This semantic deficiency is considered the root cause of the three major…

We prove a very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolmogorov complexity to query complexity. Our technique…

Complex logical reasoning tasks require a long sequence of reasoning, which a large language model (LLM) with chain-of-thought prompting still falls short. To alleviate this issue, neurosymbolic approaches incorporate a symbolic solver.…