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Two-Sided Strictly Locally Testable Languages

Holzer Markus, Kutrib Martin, Otto Friedrich

Fundamenta Informaticae

2021

Vol. 180, nr 1-2

29--51

A two-sided extension of strictly locally testable languages is presented. In order to determine membership within a two-sided strictly locally testable language, the input must be scanned from both ends simultaneously, whereby it is synchronously checked that the factors read are correlated with respect to a given binary relation. The class of two-sided strictly locally testable languages is shown to be a proper subclass of the even linear languages that is incomparable to the regular languages with respect to inclusion. Furthermore, closure properties of the class of two-sided strictly locally testable languages and decision problems are studied. Finally, it is shown that two-sided strictly k-testable languages are learnable in the limit from positive data.

Simple SubTypes of Intersection Types

Statman Rick

Fundamenta Informaticae

2019

Vol. 170, nr 1-3

307--324

Solving the Entscheidungsproblem was a challenge first posed by David Hilbert in 1928, and solutions to decision problems are perhaps the most prized posessions in logic. Pawel Urzyczyn has a number of these, one of which I will discuss below. However, let me remind you of Michael Rabin describing his time with Dana Scott at IBM prior to their Turing award winning paper Finite automata and their decision problems “So we both went, in 1957 to IBM and the location was the so-called Lamb Estate [Robert S. Lamb estate], a wonderful place, while the Princeton Laboratory, designed by Sarason, the Watson Laboratory was in stages of construction. The Lamb Estate, very appropriately, used to be, before that, an Insane Asylum. All those buildings were building where kooks were housed...” [1]. This is what IBM thought of decision problems. In this note we give a new proof of the undecidability of the inhabitation problem for intersection types.

Applying Modern SAT-solvers to Solving Hard Problems

Niewiadomski Artur, Switalski Piotr, Sidoruk Teofil, Penczek Wojciech

Fundamenta Informaticae

2019

Vol. 165, nr 3-4

321--344

We present nine SAT-solvers and compare their efficiency for several decision and combinatorial problems: three classical NP-complete problems of the graph theory, bounded Post correspondence problem (BPCP), extended string correction problem (ESCP), two popular chess problems, PSPACE-complete verification of UML systems, and the Towers of Hanoi (ToH) of exponential solutions. In addition to several known reductions to SAT for the problems of graph k-colouring, vertex k-cover, Hamiltonian path, and verification of UML systems, we also define new original reductions for the N-queens problem, the knight’s tour problem, and ToH, SCP, and BPCP. Our extensive experimental results allow for drawing quite interesting conclusions on efficiency and applicability of SAT-solvers to different problems: they behave quite efficiently for NP-complete and harder problems but they are by far inferior to tailored algorithms for specific problems of lower complexity.