Related papers: Insignificant Choice Polynomial Time: A Logic Capt…

We extend Choiceless Polynomial Time (CPT), the currently only remaining promising candidate in the quest for a logic capturing PTime, so that this extended logic has the following property: for every class of structures for which…

Abstract State Machines (ASMs) provide a model of computations on structures rather than strings. Blass, Gurevich and Shelah showed that deterministic PTIME-bounded ASMs define the choiceless fragment of PTIME, but cannot capture PTIME. In…

The search for a logic capturing PTIME is a long standing open problem in finite model theory. One of the most promising candidate logics for this is Choiceless Polynomial Time with counting (CPT). Abstractly speaking, CPT is an…

Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model…

Choiceless Polynomial Time (CPT) is one of the few remaining candidate logics for capturing PTIME. In this paper, we make progress towards separating CPT from polynomial time by firstly establishing a connection between the expressive power…

This paper extends prior work on the connections between logics from finite model theory and propositional/algebraic proof systems. We show that if all non-isomorphic graphs in a given graph class can be distinguished in the logic…

The central open question in Descriptive Complexity is whether there is a logic that characterizes deterministic polynomial time (PTIME) on relational structures. Towards this goal, we define a logic that is obtained from first-order logic…

Fixed-parameter algorithms, approximation algorithms and moderately exponential algorithms are three major approaches to algorithms design. While each of them being very active in its own, there is an increasing attention to the connection…

Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are…

The halting problem for Turing machines is decidable on a set of asymptotic probability one. Specifically, there is a set B of Turing machine programs such that (i) B has asymptotic probability one, so that as the number of states n…

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…

We use the technique of coherent population trapping (CPT) to access the ground hyperfine interval (clock transition) in $^{133}$Cs. The probe and control beams required for CPT are obtained from a single compact diode laser system. The…

Standard one-way quantum computers (1WQC) combine time symmetric unitary evolution, with asymmetric treatment of boundaries: state preparation allows to enforce a chosen initial state, however, for the final state measurement chooses a…

This paper introduces new notions of asymptotic proofs, PT(polynomial-time)-extensions, PTM(polynomial-time Turing machine)-omega-consistency, etc. on formal theories of arithmetic including PA (Peano Arithmetic). This paper shows that P…

We present a type system for an extension of lambda calculus with a conditional construction, named STAB, that characterizes the PSPACE class. This system is obtained by extending STA, a type assignment for lambda-calculus inspired by…

$\mathcal{PT}$-symmetric systems have garnered significant attention due to their unconventional properties. Despite the growing interest, there remains an ongoing debate about whether these systems outperform their Hermitian counterparts…

Modeling time related aspects is important in many applications of verification methods. For precise results, it is necessary to interpret time as a dense domain, e.g. using timed automata as a formalism, even though the system's resulting…

The classification and construction of symmetry protected topological (SPT) phases have been intensively studied in interacting systems recently. To our surprise, in interacting fermion systems, there exists a new class of the so-called…

We give a characterization of deterministic polynomial time computation based on an algebraic structure called the resolution semiring, whose elements can be understood as logic programs or sets of rewriting rules over first-order terms.…

Constraint Satisfaction Problem on finite sets is known to be NP-complete in general but certain restrictions on the constraint language can ensure tractability. It was proved that if a constraint language has a weak near unanimity…