@incollection{, DF6DDA77000C7FDE3CDFC0016D4C33B4 , author={{StarchakM.R} and {KosovskiiN.K.} and {KosovskayaT.M.} and {St. Petersburg State University}}, journal={{Global Journal of Computer Science and Technology}}, journal={{GJCST}}0975-41720975-435010.34257/gjcst, address={Cambridge, United States}, publisher={Global Journals Organisation}1742125 } @book{b0, , title={{Algorithmic number theory, I: Efficient algorithms}} , author={{ EBach } and { JShallit }} , year={1996} , publisher={MIT Press} , address={Cambridge, MA} } @incollection{b1, , title={{Bounds on positive integral solutions of linear diophantine equations}} , author={{ IBorosh } and { LBTreybig }} , journal={{Proceedings of the American Mathematical Society}} 55 2 , year={1976} } @incollection{b2, , title={{On parametric timed automata and one-counter machines}} , author={{ DBundala } and { JOuaknine }} , journal={{Information and Computation}} 253 , year={2017} } @incollection{b3, , title={{The laws of integer divisibility, and solution sets of linear divisibility conditions}} , author={{ LVan Den Dries } and { AJWilkie }} , journal={{Journal of Symbolic Logic}} 68 2 , year={2003} } @incollection{b4, , title={{Graph layout problems parameterized by vertex cover}} , author={{ MRFellows } and { DLokshtanov } and { NMisra } and { FARosamond } and { SSaurabh }} , booktitle={{Proceedings of the 19th International Symposium on Algorithms and Computation}} the 19th International Symposium on Algorithms and Computation , year={2008} } @book{b5, , title={{Computers and Intractability: A guide to the theory of NPcompleteness}} , author={{ MRGarey } and { DSJohnson }} , year={1979} , publisher={W. H. Freeman and co} , address={New York} } @incollection{b6, , title={{Subclasses of Presburger arithmetic and the weak EXP hierarchy}} , author={{ CHaase }} , booktitle={{Proceedings of the Joint Meeting of the 23rd EACSL Annual Conference on Computer Science Logic and the 29th Annual IEEE Symposium on Logic in Computer Science}} the Joint Meeting of the 23rd EACSL Annual Conference on Computer Science Logic and the 29th Annual IEEE Symposium on Logic in Computer Science , year={2014} } @incollection{b7, , title={{NP-completeness conditions for verifying the consistency of several kinds of systems of linear diophantine discongruences}} , author={{ NKKosovskii } and { TMKosovskaya } and { NNKosovskii }} , booktitle={{Vestnik SPbSU. Mathematics. Mechanics. Astronomy}} 49 1 , year={2016} } @book{b8, , title={{NP-completeness conditions for verifying the consistency of several kinds of systems of linear diophantine dis-equations}} , author={{ NKKosovskii } and { TMKosovskaya } and { NNKosovskii }} , publisher={Vestnik SPbSU} } @incollection{b9, , title={{}} , journal={{Mathematics. Mechanics. Astronomy}} 49 3 , year={2016} } @incollection{b10, , title={{NP-complete problems for systems of divisibilities of values of linear polynomials}} , author={{ NKKosovskii } and { TMKosovskaya } and { NNKosovskii } and { MRStarchak }} , booktitle={{Vestnik SPbSU. Mathematics. Mechanics}} } @incollection{b11, , title={{}} , journal={{Astronomy}} 4 62 , year={2017} } @incollection{b12, , title={{Synthesis problems for one-counter automata}} , author={{ ALechner }} , booktitle={{Proceedings of 9th International Workshop on Reachability Problems}} 9th International Workshop on Reachability Problems , year={2015} } @incollection{b13, , title={{On the complexity of linear arithmetic with divisibility}} , author={{ ALechner } and { JOuaknine } and { JWorrell }} , booktitle={{Proceedings of 30th Annual IEEE Symposium on Logic in Computer Science}} 30th Annual IEEE Symposium on Logic in Computer Science , year={2015} } @incollection{b14, , title={{Integer programming with a fixed number of variables}} , author={{ HW JLenstra }} , journal={{Mathematics of Operations Research}} 8 4 , year={1983} } @incollection{b15, , title={{Some remarks on the diophantine problem for addition and divisibility}} , author={{ LLipshitz }} , journal={{Bulletin de la Société mathématique de Belgique. Série B}} 33 1 , year={1981} } @incollection{b16, , title={{Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt}} , author={{ MPresburger }} , booktitle={{Comptes rendus du 1er Congrès des Mathématiciens des Pays Slaves}} , year={1929} } @incollection{b17, , title={{What are weak arithmetics?}} , author={{ DRichard }} , booktitle={{Theoretical Computer Science}} , year={2001} 257 } @book{b18, , title={{Some problems in logic and number theory, and their connections}} , author={{ AWoods }} , year={1981} University of Manchester , note={PhD Thesis} , note={the case of every term from this theory of the form ? ..} }