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Fundamenta Informaticae is an international journal publishing original research results in all areas of theoretical computer science. Papers are encouraged contributing:
- solutions by mathematical methods of problems emerging in computer science
- solutions of mathematical problems inspired by computer science.
Topics of interest include (but are not restricted to): theory of computing, complexity theory, algorithms and data structures, computational aspects of combinatorics and graph theory, programming language theory, theoretical aspects of programming languages, computer-aided verification, computer science logic, database theory, logic programming, automated deduction, formal languages and automata theory, concurrency and distributed computing, cryptography and security, theoretical issues in artificial intelligence, machine learning, pattern recognition, algorithmic game theory, bioinformatics and computational biology, quantum computing, probabilistic methods, & algebraic and categorical methods.
Authors: Janicki, Ryszard
Article Type: Research Article
Abstract: A mathematical model for recursive coroutines in introduced. Relationships between Mazurkiewicz algorithms and this model are considered. Some linguistic and computational properties of coroutines are proved. The set of all functions computed by programs with recursive coroutines is proved to contain the set of all functions computed by commonly used recursive programs.
DOI: 10.3233/FI-1977-1110
Citation: Fundamenta Informaticae, vol. 1, no. 1, pp. 131-145, 1977
Authors: Mirkowska, Grażyna
Article Type: Research Article
DOI: 10.3233/FI-1977-1111
Citation: Fundamenta Informaticae, vol. 1, no. 1, pp. 147-165, 1977
Authors: Banachowski, Lech
Article Type: Research Article
DOI: 10.3233/FI-1977-1112
Citation: Fundamenta Informaticae, vol. 1, no. 1, pp. 167-193, 1977
Authors: Kreczmar, Antoni
Article Type: Research Article
Abstract: In the present paper we investigate algorithmic properties of fields. We prove that axioms of formally real fields for the field R of reals and axioms of fields of characteristic zero for the field C of complex numbers, give the complete characterization of algorithmic properties. By Kfoury’s theorem programs which define total functions over R or C are effectively equivalent to loop-free programs. Examples of programmable and nonprogrammable functions and relations over R and C are given. In the case of ordered reals the axioms of Archimedean ordered …fields completely characterize algorithmic properties. We show how to use the equivalent version of Archimed’s axiom (the exhaustion rule) in order to prove formally the correctness of some iterative numerical algorithms. Show more
Keywords: programs and programmability, algorithmic properties, programmability in fields, axioms for algorithmic properties of reals, ordered reals and complex numbers
DOI: 10.3233/FI-1977-1113
Citation: Fundamenta Informaticae, vol. 1, no. 1, pp. 195-230, 1977
Authors: Janicki, Sławomir | Szynal, Dominik
Article Type: Research Article
Abstract: There are a great many research works concerning the well-known stochastic automata of Moore, Mealy, Rabin, Turing and others. Recently an automaton of Markov’s chain type has been introduced by Bartoszyński. This automaton is obtained by a generalization of Pawlak’s deterministic machine. The aim of this note is to give a concept of a stochastic automaton of Markov’s generalized chain type. The introduced automaton called a stochastic k -automaton (s.k -a.) is a common generalization of Bartoszyński’s automaton and Grodzki’s deterministic k -machine. By a stochastic k -automaton we mean an ordered triple M k …= ⟨ U , a , π ⟩ , k ⩾ 1 , where U denotes a finite non-empty set, a is a function from U k to [0, 1] with ∑ v ∈ U k a ( v ) = 1 , and π is a function from U k+1 to [0,1] with ∑ u ∈ U π ( v , u ) = 1 for every v ∈ U k . For all N ⩾ k we can define a probability measure P N on U N = U × U × … × U as follows: P N ( u 1 , u 2 , … , u N ) = a ( u 1 , u 2 , … , u k ) π ( u 1 , u 2 , … , u k + 1 ) π ( u 2 , u 3 , … , u k + 2 ) … π ( u N − k , u N − k + 1 , … , u N ) . We deal with the problems of the shrinkage and the extension of a system of s.k-a .’s M k ( i ) = ⟨ U , a ( i ) , π ( i ) ⟩ , i = 1 , 2 , … , m , m ⩾ 2 . In this note there are given conditions under which an s.k -a. M k = ⟨ U , a , π ⟩ exists and the language of this automaton defined as L M = { ( u 1 , u 2 , u 3 , … ) : ∧ N ⩾ 1 P N ( u l , u 2 , … u N ) > 0 } either contains the languages of all the automata M k ( i ) , i = 1 , 2 , … , m , or this language equals the intersection of all those languages. Show more
Keywords: stochastic k-automaton, extension, shrinkage, N-word, set of N-words, words, language, probability measure, carrier, concordance, truly concordance, pairwise concordance
DOI: 10.3233/FI-1977-1114
Citation: Fundamenta Informaticae, vol. 1, no. 1, pp. 231-241, 1977
Authors: Karásek, Jiří
Article Type: Research Article
Abstract: The paper deals with nondeterministic and deterministic k -machines which represent, in a certain sense, generalizations of some well-known notions. Connections between the sets of sequences constructed by nondeterministic and deterministic k -machines, and some other related problems are investigated.
Keywords: deterministic machines, nondetcrministic machines, finite automata
DOI: 10.3233/FI-1977-1115
Citation: Fundamenta Informaticae, vol. 1, no. 1, pp. 243-250, 1977
Authors: Aiello, Luigia | Aiello, Mario | Attardi, Giuseppe | Prini, Gianfranco
Article Type: Research Article
Abstract: An interactive proof checker is a system which is able of building a formal proof (in some deductive calculus) by executing commands provided by the user. Proof checkers are useful both for making experiments in proof construction within various formal systems and for proving theorems in those fields of mathematics (such as mathematical theory of computation) where proofs are necessarily very large and unfeasible by hand. Two levels may be distinguished in a proof checker. The lower one implements the proof management routines, and is independent of any particular logic. The higher one implements the inference rules of a particular …logical calculus. Powerful higher level rules are also needed to make the use of the checker practical. Almost all routine steps may be then generated automatically, and the user has just to give some “hints” to the checker, which transforms an “informal argument” into a formal proof. Show more
Keywords: automatic theorem proving, denotational semantics of programming languages, mathematical theory of computation, proof of formal properties of programs
DOI: 10.3233/FI-1977-1116
Citation: Fundamenta Informaticae, vol. 1, no. 1, pp. 251-275, 1977
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