Related papers: Proof Systems Based on Structured Circuits
In sphere of research of discrete optimization algorithms efficiency the important place occupies a method of polynomial reducibility of some problems to others with use of special purpose components. In this paper a novel method of compact…
Deep neural networks (DNNs) and decision trees (DTs) are both state-of-the-art classifiers. DNNs perform well due to their representational learning capabilities, while DTs are computationally efficient as they perform inference along one…
Automatic synthesis of hardware components from declarative specifications is an ambitious endeavor in computer aided design. Existing synthesis algorithms are often implemented with Binary Decision Diagrams (BDDs), inheriting their…
A common theme in factorised databases and knowledge compilation is the representation of solution sets in a useful yet succinct data structure. In this paper, we study the representation of the result of join queries (or, equivalently, the…
Decomposable Negation Normal Forms \textsc{dnnf} [Darwiche, 'Decomposable Negation Normal Form', JACM, 2001] is a landmark Knowledge Compilation (\textsc{kc}) model, highly important both in \textsc{ai} and Theoretical Computer Science.…
This paper proposes a new logic optimization paradigm based on circuit simulation, which reduces the need for Boolean computations such as SAT-solving or constructing BDDs. The paper develops a Boolean resubstitution framework to…
In recent years numerous methods have been developed to formally verify the robustness of deep neural networks (DNNs). Though the proposed techniques are effective in providing mathematical guarantees about the DNNs behavior, it is not…
During the last decade, deep neural networks (DNN) have demonstrated impressive performances solving a wide range of problems in various domains such as medicine, finance, law, etc. Despite their great performances, they have long been…
A central task in knowledge compilation is to compile a CNF-SAT instance into a succinct representation format that allows efficient operations such as testing satisfiability, counting, or enumerating all solutions. Useful representation…
The intersection of numerical analysis and machine learning, particularly in the domain of Neural ODEs and Physics-Informed Neural Networks (PINNs), relies heavily on discrete approximations of continuous flows. However, in stiff systems,…
We exhibit families of $4$-CNF formulas over $n$ variables that have sums-of-squares (SOS) proofs of unsatisfiability of degree (a.k.a. rank) $d$ but require SOS proofs of size $n^{\Omega(d)}$ for values of $d = d(n)$ from constant all the…
Neural networks are powerful function estimators, leading to their status as a paradigm of choice for modeling structured data. However, unlike other structured representations that emphasize the modularity of the problem -- e.g., factor…
Cause-consequence Diagram (CCD) is widely used as a deductive safety analysis technique for decision-making at the critical-system design stage. This approach models the causes of subsystem failures in a highly-critical system and their…
Many problems can be specified by patterns of propositional formulae depending on a parameter, e.g. the specification of a circuit usually depends on the number of bits of its input. We define a logic whose formulae, called "iterated…
The goal of this paper is to establish that it remains undecidable whether a sequent is provable in two systems in which a weakening rule for an exponential modality is completely omitted from classical propositional linear logic…
This paper studies node classification in the inductive setting, i.e., aiming to learn a model on labeled training graphs and generalize it to infer node labels on unlabeled test graphs. This problem has been extensively studied with graph…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
Selman and Kautz's work on ``knowledge compilation'' established how approximation (strengthening and/or weakening) of a propositional knowledge-base can be used to speed up query processing, at the expense of completeness. In this…
Neural networks have emerged as essential components in safety-critical applications -- these use cases demand complex, yet trustworthy computations. Binarized Neural Networks (BNNs) are a type of neural network where each neuron is…
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…