Related papers: On proof theory in computer science
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a…
In this paper we present a more transparent upgrade of our proofs and comment on Jerabek's paper [8].
In this paper, we investigate the proof complexity of a wide range of substructural systems. For any proof system $\mathbf{P}$ at least as strong as Full Lambek calculus, $\mathbf{FL}$, and polynomially simulated by the extended Frege…
We survey lower-bound results in complexity theory that have been obtained via newfound interconnections between propositional proof complexity, boolean circuit complexity, and query/communication complexity. We advocate for the theory of…
Contexts are terms with one `hole', i.e. a place in which we can substitute an argument. In context unification we are given an equation over terms with variables representing contexts and ask about the satisfiability of this equation.…
One of the central open problems to classify the computational complexity of finite-domain constraint satisfaction problems within P is to prove better algorithmic results for CSPs with a Maltsev polymorphism; we do not even know whether…
We consider logic-based argumentation in which an argument is a pair (Fi,al), where the support Fi is a minimal consistent set of formulae taken from a given knowledge base (usually denoted by De) that entails the claim al (a formula). We…
We investigate the computational complexity of admissibility of inference rules in infinite-valued {\L}ukasiewicz propositional logic (\L). It was shown in [13] that admissibility in {\L} is checkable in PSPACE. We establish that this…
Rice's Theorem states that every nontrivial language property of the recursively enumerable sets is undecidable. Borchert and Stephan initiated the search for complexity-theoretic analogs of Rice's Theorem. In particular, they proved that…
The CSP (constraint satisfaction problems) is a class of problems deciding whether there exists a homomorphism from an instance relational structure to a target one. The CSP dichotomy is a profound result recently proved by Zhuk (2020, J.…
Viewing formal mathematical proofs as logical terms provides a powerful and elegant basis for analyzing how human experts tend to structure proofs and how proofs can be structured by automated methods. We pursue this approach by (1)…
We present quantitative logics with two-step semantics based on the framework of quantitative logics introduced by Arenas et al. (2020) and the two-step semantics defined in the context of weighted logics by Gastin & Monmege (2018). We show…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
One way of suggesting that an NP problem may not be NP-complete is to show that it is in the class UP. We suggest an analogous new approach---weaker in strength of evidence but more broadly applicable---to suggesting that concrete~NP…
Until now, Computer Scientists have concerned themselves with identifying efficient algorithms for solving the general case of some problem -- that is finding one which performs well when the size of the input tends to infinity. In this…
We establish new, and surprisingly tight, connections between propositional proof complexity and finite model theory. Specifically, we show that the power of several propositional proof systems, such as Horn resolution, bounded-width…
The $P$ versus $NP$ problem is still unsolved. But there are several oracles with $P$ unequal $NP$ relative to them. Here we will prove, that $P\not=NP$ relative to a $P$-complete oracle. In this paper, we use padding arguments as the proof…
We show that every NP problem is polynomially equivalent to a simple combinatorial problem: the membership problem for a special class of digraphs. These classes are defined by means of shadows (projections) and by finitely many forbidden…
Over the course of the last 50 years, many questions in the field of computability were left surprisingly unanswered. One example is the question of $P$ vs $NP\cap co-NP$. It could be phrased in loose terms as "If a person has the ability…