title: Extraction of a maximal common sub-formula of predicate formulas for the solving of some Artificial Intelligence problems
metadata.name: dc.contributor.author
metadata.value: Kosovskaya, Tatiana M.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Petrov, Dmitrii A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-10-12T09:37:19Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-10-12T09:37:19Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Kosovskaya T. M., Petrov D. A. Extraction of a maximal common sub-formula of predicate formulas for the solving of some Artificial Intelligence problems. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2017, vol. 13, iss. 3, pp. 250–263.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu10.2017.303
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/8511
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: If an investigated object in an Artificial Intelligence problem is regarded as a set of its elements
  and is characterized by properties of these elements and relations between them, then a predicate
  calculus language is an adequate one for the description of an object and classes of objects.
  Such a way formalized problems are NP-complete or NP-hard. Example of such an NP-hard
  problem is the problem of the analysis of a complex object presented as a set of its elements
  and described by a set of atomic formulas with the predicates setting properties of these
  elements and relation between them. To solve such a problem, a problem of extraction of a
  maximal common up to the names of variables sub-formula of two elementary conjunctions
  of atomic predicate formulas is under consideration in the paper. Extraction of these subformulas
  allows us to reduce a recognition problem to a series of analogous problems with the
  less input data length by means of construction a level description of classes, which essentially
  decreases an exponent in the exponential upper bound for a number of solution algorithm steps
  for NP-hard problem of checking whether an object belongs to this class. An algorithm of
  extraction of a maximal common up to the names of variables sub-formula of two elementary
  conjunctions of atomic predicate formulas is presented in the paper. Bounds on number of the
  algorithm run number of steps are proved. The time of its implementation in dependence on
  the input data structure is analyzed. The analysis of the number of algorithm steps shows that
  the proposed algorithm may be successfully implemented in order to decrease computational
  complexity of many Artificial Intelligence problems which are formalized by means of predicate
  calculus. The results of numerical experiments show the influence of input data structure
  on the algorithm run time. For example, the increasing of amount of predicate arguments
  involves essential decreasing of the algorithm run time, which is a consequence of the recursion
  depth decreasing. The number of different predicate symbols occurred in the formula notation
  also essentially influences on the algorithm run time. At larger input data the effectiveness of
  the offered algorithm, cutting obviously unsuccessful “brunches”, is especially noticeable. The
  strong impact on the algorithm run time is exerted by distribution of variables as arguments of
  predicates. Results show its considerable decreasing at a nonuniform distribution of variables.
  During the described algorithm run a problem of checking the coincidence up to the names of
  variables (isomorphism) of two elementary conjunctions appears. This problem has the greatest
  computational complexity among the other problems arising on other steps of the algorithm.
  A polynomial algorithm of checking whether two elementary conjunctions of atomic predicate
  formulas coincide up to the names of variables (are isomorphic) is offered. The algorithm is not
  a precise one. The correctness of this algorithm implementation exceeds 99,5%. It is proved that
  if the algorithm gives a negative answer then the formulas are not isomorphic. If the algorithm
  gives a positive answer then the results of numerical experiments show that 99,5% pairs of
  formulas are isomorphic. Refs 14. Tables 2.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 13; Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: Artificial Intelligence
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: predicate calculus
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: algorithmic complexity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: isomorphism of predicate formulas
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Extraction of a maximal common sub-formula of predicate formulas for the solving of some Artificial Intelligence problems
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 03-Kosovskaya.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/8511/1/03-Kosovskaya.pdf
resources.format: Adobe PDF
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