Related papers: A Complete Proof System for 1-Free Regular Express…
The action of a noise operator on a code transforms it into a distribution on the respective space. Some common examples from information theory include Bernoulli noise acting on a code in the Hamming space and Gaussian noise acting on a…
Examples of discontinuous functions already appear in the work of Euler, Abel, Dirichlet, Fourier, and Bolzano. A ground-breaking discovery due to Baire was that many discontinuous functions are well-behaved in that they are the pointwise…
Given an associative, not necessarily commutative, ring R with identity, a formal matrix calculus is introduced and developed for pairs of matrices over R. This calculus subsumes the theory of homogeneous systems of linear equations with…
We prove that the relation of bisimilarity between countable labelled transition systems is $\Sigma_1^1$-complete (hence not Borel), by reducing the set of non-wellorders over the natural numbers continuously to it. This has an impact on…
Even the fastest SMT solvers have performance problems with regular expressions from real programs. Because these performance issues often arise from the problem representation (e.g. non-deterministic finite automata get determinized and…
Kleene algebra (KA) is an important tool for reasoning about general program equivalences, with a decidable and complete equational theory. However, KA cannot always prove equivalences between specific programs. For this purpose, one adds…
We introduce a high-level language with Python-like syntax for string-to-string, polyregular, first-order definable transductions. This language features function calls, boolean variables, and nested for-loops. We devise and implement a…
Extending and generalizing the approach of 2-sequents (Masini, 1992), we present sequent calculi for the classical modal logics in the K, D, T, S4 spectrum. The systems are presented in a uniform way-different logics are obtained by tuning…
Many formal languages include binders as well as operators that satisfy equational axioms, such as commutativity. Here we consider the nominal language, a general formal framework which provides support for the representation of binders,…
This paper continues the author's previous study \cite{Kura20}, showing that several weak principles inspired by non-normal modal logic suffice to derive various refined forms of the second incompleteness theorem. Among the main results of…
We develop a practical framework for livelock analysis in self-disabling unidirectional ring protocols. Klinkhamer and Ebnenasir established that livelock detection for parameterized rings is $\Sigma^0_1$-complete and livelock-freedom…
A recently published paper (Schmid, Rozowski, Silva, and Rot, 2022) offers a (co)algebraic framework for studying processes with algebraic branching structures and recursion operators. The framework captures Milner's algebra of regular…
In 2002 Robert Solovay proved that a subsystem BI of classical second order arithmetic, with bar induction and arithmetical countable choice, can be negatively interpreted in the neutral subsystem BSK of Kleene's intuitionistic analysis FIM…
In 2019, P. Higgins formulated [1] a question about bipartite graphs (see Conjecture 1 below); this question arises in the study of regular finite semigroups. F. V. Petrov formulated [2] another combinatorial conjecture (Conjecture 3);…
We define the concept of regularity for bigraded modules and bigraded polynomial ring. In this setting we prove analogs of some of the classical results on $m$-regularity for graded modules over polynomial algebras.
We show that every language in NP has a PCP verifier that tosses $O(\log n)$ random coins, has perfect completeness, and a soundness error of at most $1/\text{poly}(n)$, while making at most $O(\text{poly}\log\log n)$ queries into a proof…
It is well-known that extending the Hilbert axiomatic system for first-order intuitionistic logic with an exclusion operator, that is dual to implication, collapses the domains of models into a constant domain. This makes it an interesting…
Verifying whether a procedure is observationally pure is useful in many software engineering scenarios. An observationally pure procedure always returns the same value for the same argument, and thus mimics a mathematical function. The…
A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the…
We provide a sound and complete proof system for an extension of Kleene's ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of…