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23
Decision Problems For SemiThue Systems With A Few Rules
, 1996
"... For several decision problems about semiThue systems, we try to locate the frontier between the decidable and the undecidable from the point of view of the number of rules. We show that the the Termination Problem, the UTermination Problem, the Accessibility Problem and the CommonDescendant Probl ..."
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Cited by 56 (0 self)
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For several decision problems about semiThue systems, we try to locate the frontier between the decidable and the undecidable from the point of view of the number of rules. We show that the the Termination Problem, the UTermination Problem, the Accessibility Problem and the CommonDescendant Problem are undecidable for 3 rules STS. As a corollary we obtain the undecidability of the PostCorrespondence Problem for 7 rules.
Undecidable Problems for Probabilistic Automata of Fixed Dimension
 Theory of Computing Systems
, 2001
"... We prove that several problems associated to probabilistic finite automata are undecidable for automata whose number of input letters and number of states are fixed. As a corollary of one of our results we prove that the problem of determining if the set of all products of two 47 × 47 matrices ..."
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Cited by 35 (5 self)
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We prove that several problems associated to probabilistic finite automata are undecidable for automata whose number of input letters and number of states are fixed. As a corollary of one of our results we prove that the problem of determining if the set of all products of two 47 × 47 matrices with nonnegative rational entries is bounded is undecidable.
Binary (Generalized) Post Correspondence Problem
 In Proceedings of 13th STACS
, 2000
"... We give a new proof for the decidability of the binary Post Correspondence Problem (PCP) originally proved in 1982 by Ehrenfeucht, Karhumäki and Rozenberg. Our proof is complete and somewhat shorter than the original proof although we use the same basic idea. ..."
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Cited by 14 (8 self)
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We give a new proof for the decidability of the binary Post Correspondence Problem (PCP) originally proved in 1982 by Ehrenfeucht, Karhumäki and Rozenberg. Our proof is complete and somewhat shorter than the original proof although we use the same basic idea.
Mortality in Matrix Semigroups
 AMER. MATH. MONTHLY
, 2001
"... We present a new shorter and simplified proof for the undecidability of the mortality problem in matrix semigroups, originally proved by Paterson in 1970. We use the clever coding technique introduced by Paterson to achieve also a new result, the undecidability of the vanishing (left) upper corner. ..."
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Cited by 8 (5 self)
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We present a new shorter and simplified proof for the undecidability of the mortality problem in matrix semigroups, originally proved by Paterson in 1970. We use the clever coding technique introduced by Paterson to achieve also a new result, the undecidability of the vanishing (left) upper corner. Since our proof for the undecidability of the mortality problem uses only 8 matrices, a new bound for the dimension for the undecidability of the mortality in the two generator matrix semigroup is achieved.
Infinite solutions of marked Post Correspondence Problem
 FORMAL AND NATURAL COMPUTING ESSAYS DEDICATED TO GRZEGORZ ROZENBERG
, 2001
"... In an instance of the Post Correspondence Problem we are given two morphisms h; g : A ..."
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Cited by 8 (6 self)
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In an instance of the Post Correspondence Problem we are given two morphisms h; g : A
Undecidability of infinite Post correspondence problem for instances of size 9
 Theoretical Informatics and Applications
"... In the infinite Post Correspondence Problem an instance (h, g) consists of two morphisms h and g, and the problem is to determine whether or not there exists an infinite word ω such that h(ω) = g(ω). This problem was shown to be undecidable by K. Ruohonen (1985) in general. Recently V. D. Blondel a ..."
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Cited by 5 (0 self)
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In the infinite Post Correspondence Problem an instance (h, g) consists of two morphisms h and g, and the problem is to determine whether or not there exists an infinite word ω such that h(ω) = g(ω). This problem was shown to be undecidable by K. Ruohonen (1985) in general. Recently V. D. Blondel and V. Canterini (Theory Comput. Syst. 36, 231–245, 2003) showed that this problem is undecidable for domain alphabets of size 105. Here we give a proof that the infinite Post Correspondence Problem is undecidable for instances where the morphisms have domains of 9 letters. The proof uses a recent result of Matiyasevich and Sénizergues and a modification of a result of Claus. 1
Decidability and Undecidability of Marked PCP
, 1998
"... We show that the marked version of the Post Correspondence Problem, where the words on a list are required to dioeer in the rst letter, is decidable. On the other hand, if we only require the words to dioeer in the rst two letters, the problem remains undecidable. Thus we sharply locate the decidabi ..."
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Cited by 4 (3 self)
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We show that the marked version of the Post Correspondence Problem, where the words on a list are required to dioeer in the rst letter, is decidable. On the other hand, if we only require the words to dioeer in the rst two letters, the problem remains undecidable. Thus we sharply locate the decidability/undecidabilityboundary between marked and 2marked PCP. Keywords: decidability, undecidability, marked morphism, Post Correspondence Problem TUCS Research Group Theory Group: Mathematical Structures in Computer Science 1 Introduction: PCP and Marked PCP The Post Correspondence Problem (PCP) [Pos46] is one of the most useful undecidable problems, because it can be simply described and many other problems can easily be reduced to it, particularly problems in formal language theory. The general form of the problem is as follows. An instance of PCP is a fourtuple I = (\Sigma; \Delta; g; h), consisting of a nite source alphabet \Sigma = fa 1 ; : : : ; a n g, a nite target alphabet \D...
Binary Equality Set Is Generated By Two Words
, 2002
"... We show that the equality set Eq(g; h) of two nonperiodic binary morphisms g; h : is generated by at most two words. If the rank of Eq(g; h) = f; g is two, then and start and end with dierent letters. This in particular implies that any binary language has a test set of cardinality at most t ..."
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Cited by 3 (2 self)
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We show that the equality set Eq(g; h) of two nonperiodic binary morphisms g; h : is generated by at most two words. If the rank of Eq(g; h) = f; g is two, then and start and end with dierent letters. This in particular implies that any binary language has a test set of cardinality at most two. 1
Finite Substitutions and Integer Weighted Finite Automata
, 1998
"... In this work we present a new chain of undecidability reductions, which begins from the classical halting problem of Turing machines and ends to the undecidability proof of the equivalence problem for finite substitutions on regular languages in Chapter 4. This undecidability result was originally p ..."
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Cited by 2 (1 self)
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In this work we present a new chain of undecidability reductions, which begins from the classical halting problem of Turing machines and ends to the undecidability proof of the equivalence problem for finite substitutions on regular languages in Chapter 4. This undecidability result was originally proved by L. Lisovik in 1997. We present a new proof, which is shorter and more elementary than the original one. Our proof uses the undecidability of the universe problem for the integer weighted finite automata. An integer weighted nite automaton is a finite automaton, which has integer weights on its edges. This automaton accepts an input word, if there exists a path reading the word such that the sum of the weights of the used edges is zero. In the universe problem we ask whether a given integer weighted finite automaton accepts all its input words. This problem is proved undecidable in Chapter 3. The proof uses the undecidability of a certain modication of the Post Correspondence Problem, proved...