M. Davis, "Unsolvable Problems", in The Handbook of Mathematical Logic, J. Barwise (ed.), Elsevier, 1977, p. 580.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....we consider are as follows: Given an initial word W 0 , and some rules C i Gamma D i , i = 1 Delta Delta Delta n, can we derive a word W Proposition 2 There is a word W 0 and rules C i Gamma D i such that the problem of determining if a word W can be derived is undecidable. Proof In [2], a universal Turing machine is encoded as a semi Thue system so as to give a set of rules F i and a word W 0 such that the problem Given a word W , can W 0 be derived from W is undecidable. By reversing all the rules of this problem, we get the proposition, except with a larger alphabet. It is ....

M. Davis. Unsolvable Problems, in J. Barwise, editor, The Handbook of Mathematical Logic. North-Holland, 1977.

....NP complete by Levin [Lev86] but only a proof sketch was given. A detailed proof for tiles with marked edges was given in [Gur91] see also [BW93, WB95] 3. 3 Distributional Post Correspondence and Related Problems The Post correspondence problem was first studied by Post (see, for example, [Dav77]) which is to decide, when given a nonempty list L = h(u 1 ; v 1 ) um ; v m )i of pairs of binary strings, whether there is a sequence of integers i 1 ; i 2 ; i k , with k 1, such that u i 1 u i 2 Delta Delta Delta u i k = v i 1 v i 2 Delta Delta Delta v i k . The sequence i ....

M. Davis, Unsolvable problems. In Jon Barwise, editor, Handbook of Mathematical Logic, pages 567--594, North-Holland, 1977.

....for deciding if the Turing machine of f halts for a given input. 4 Undecidability of the ACD ground word problem Given a Turing machine, we are going to encode its halting problem into an ACD ground word problem. Our method is similar to the proof of undecidability of the A ground word problem [5]. In this proof, a configuration of the machine is coded by a word on a certain alphabet. Here we don t have any associative operator so we can t use words. The important property of words is that they are ordered sequences of letters. Here we are going to use polynomials, where the coefficients ....

Martin Davis. Unsolvable problems. In J. Barwise, editor, Handbook of Mathematical Logic, pages 567--594. North-Holland, 1977.

.... termination results for quotients of finite trees It is not possible to expect termination and completeness results when A is an arbitrary quotient of T (F ) This would indeed imply in particular the decidability of unification modulo any set of equational axioms which is known to be undecidable [Dav77]. It is not even possible to find a semi decision procedure for the satisfiability of equational formulas in any quotient of T (F ) since the first order theory of T (F ) E is complete. Hence, such a semi decision procedure would imply the decidability of theory (see section 4) This is the ....

Martin Davis. Unsolvable problems. In J. Barwise, editor, Handbook of Mathematical Logic, pages 567--594. North-Holland, 1977.

....that guarantee the congruence property of the operations on strings. The starting point of the method proposed is the undecidability of Post s Correspondence Problem. Of course there are many other undecidable problems that might serve for reduction to the decision problem of a theory (see Davis (1977)) One may, for instance, take the uniform halting problem for Turing machines and perform a reduction proof in the above style: A Turing machine halts iff there is a finite sequence of configurations such that the first and the last one are in some special form and such that each adjacent pair is ....

Davis, M. (1977). Unsolvable problems. In Barwise, J., editor, Handbook of Mathematical Logic, chapter C.2, pages 567--594. North-Holland.

....Theorem 4.4 The following problem is in general undecidable: ffl Given a finite signature Sigma and a finite set of identities E. ffl Is ( Sigma; E) monoidal (resp. commutative) We shall reduce a known undecidable problem for monoids and groups to this problem. It is well known (see, e.g. [10], Corollary 3.8) that for finitely presented groups it is in general undecidable whether the group is trivial (i.e. consists of only one element) or not. Since finitely presented groups are a special case of finitely presented monoids, this undecidability result holds for monoids as well. Now ....

Davis, M.: Unsolvable Problems. In: Barwise, J. (ed.) Handbook of Mathematical Logic. Amsterdam: Elsevier Science Publishers 1977

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M. Davis, "Unsolvable Problems", in The Handbook of Mathematical Logic, J. Barwise (ed.), Elsevier, 1977, p. 580.

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M. Davis. Unsolvable Problems. in: J. Barwise (ed.), Handbook of Mathematical Logic, North Holland, Amsterdam, 1977.

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M. Davis. Unsolvable Problems. In J. Barwise, editor, The Handbook of Mathematical Logic. North-Holland, 1977.

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