Is LocalDB supported in WinHost?

I guess the answer is no, but want to double check.

I created a website using LocalDB. In my machine everything works fine, but when publishing the website, I get the following error.

Code:

[Win32Exception (0x80004005): The system cannot find the file specified]

[SqlException (0x80131904): A network-related or instance-specific error occurred while establishing a connection to SQL Server. The server was not found or was not accessible. Verify that the instance name is correct and that SQL Server is configured to allow remote connections. (provider: SQL Network Interfaces, error: 52 - Unable to locate a Local Database Runtime installation. Verify that SQL Server Express is properly installed and that the Local Database Runtime feature is enabled.)]
   System.Data.SqlClient.SqlInternalConnection.OnError(SqlException exception, Boolean breakConnection, Action`1 wrapCloseInAction) +5296071
   System.Data.SqlClient.TdsParser.ThrowExceptionAndWarning(TdsParserStateObject stateObj, Boolean callerHasConnectionLock, Boolean asyncClose) +558
   System.Data.SqlClient.TdsParser.Connect(ServerInfo serverInfo, SqlInternalConnectionTds connHandler, Boolean ignoreSniOpenTimeout, Int64 timerExpire, Boolean encrypt, Boolean trustServerCert, Boolean integratedSecurity, Boolean withFailover) +5308555
   System.Data.SqlClient.SqlInternalConnectionTds.AttemptOneLogin(ServerInfo serverInfo, String newPassword, SecureString newSecurePassword, Boolean ignoreSniOpenTimeout, TimeoutTimer timeout, Boolean withFailover) +145
   System.Data.SqlClient.SqlInternalConnectionTds.LoginNoFailover(ServerInfo serverInfo, String newPassword, SecureString newSecurePassword, Boolean redirectedUserInstance, SqlConnectionString connectionOptions, SqlCredential credential, TimeoutTimer timeout) +920
   System.Data.SqlClient.SqlInternalConnectionTds.OpenLoginEnlist(TimeoutTimer timeout, SqlConnectionString connectionOptions, SqlCredential credential, String newPassword, SecureString newSecurePassword, Boolean redirectedUserInstance) +307
   System.Data.SqlClient.SqlInternalConnectionTds..ctor(DbConnectionPoolIdentity identity, SqlConnectionString connectionOptions, SqlCredential credential, Object providerInfo, String newPassword, SecureString newSecurePassword, Boolean redirectedUserInstance, SqlConnectionString userConnectionOptions) +434
   System.Data.SqlClient.SqlConnectionFactory.CreateConnection(DbConnectionOptions options, DbConnectionPoolKey poolKey, Object poolGroupProviderInfo, DbConnectionPool pool, DbConnection owningConnection, DbConnectionOptions userOptions) +225
   System.Data.ProviderBase.DbConnectionFactory.CreatePooledConnection(DbConnectionPool pool, DbConnectionOptions options, DbConnectionPoolKey poolKey, DbConnectionOptions userOptions) +37
   System.Data.ProviderBase.DbConnectionPool.CreateObject(DbConnectionOptions userOptions) +558
   System.Data.ProviderBase.DbConnectionPool.UserCreateRequest(DbConnectionOptions userOptions) +67
   System.Data.ProviderBase.DbConnectionPool.TryGetConnection(DbConnection owningObject, UInt32 waitForMultipleObjectsTimeout, Boolean allowCreate, Boolean onlyOneCheckConnection, DbConnectionOptions userOptions, DbConnectionInternal& connection) +1052
   System.Data.ProviderBase.DbConnectionPool.TryGetConnection(DbConnection owningObject, TaskCompletionSource`1 retry, DbConnectionOptions userOptions, DbConnectionInternal& connection) +78
   System.Data.ProviderBase.DbConnectionFactory.TryGetConnection(DbConnection owningConnection, TaskCompletionSource`1 retry, DbConnectionOptions userOptions, DbConnectionInternal& connection) +167
   System.Data.ProviderBase.DbConnectionClosed.TryOpenConnection(DbConnection outerConnection, DbConnectionFactory connectionFactory, TaskCompletionSource`1 retry, DbConnectionOptions userOptions) +143
   System.Data.SqlClient.SqlConnection.TryOpen(TaskCompletionSource`1 retry) +83
   System.Data.SqlClient.SqlConnection.Open() +96
   System.Data.Entity.SqlServer.<>c__DisplayClass2f.<UsingConnection>b__2d() +73
   System.Data.Entity.SqlServer.<>c__DisplayClass1.<Execute>b__0() +10
   System.Data.Entity.SqlServer.DefaultSqlExecutionStrategy.Execute(Func`1 operation) +189
   System.Data.Entity.SqlServer.DefaultSqlExecutionStrategy.Execute(Action operation) +78
   System.Data.Entity.SqlServer.SqlProviderServices.UsingConnection(DbConnection sqlConnection, Action`1 act) +229
   System.Data.Entity.SqlServer.SqlProviderServices.UsingMasterConnection(DbConnection sqlConnection, Action`1 act) +376
   System.Data.Entity.SqlServer.SqlProviderServices.GetDbProviderManifestToken(DbConnection connection) +201
   System.Data.Entity.Core.Common.DbProviderServices.GetProviderManifestToken(DbConnection connection) +85

[ProviderIncompatibleException: The provider did not return a ProviderManifestToken string.]
   System.Data.Entity.Core.Common.DbProviderServices.GetProviderManifestToken(DbConnection connection) +269
   System.Data.Entity.Utilities.DbProviderServicesExtensions.GetProviderManifestTokenChecked(DbProviderServices providerServices, DbConnection connection) +33

[ProviderIncompatibleException: An error occurred while getting provider information from the database. This can be caused by Entity Framework using an incorrect connection string. Check the inner exceptions for details and ensure that the connection string is correct.]
   System.Data.Entity.Utilities.DbProviderServicesExtensions.GetProviderManifestTokenChecked(DbProviderServices providerServices, DbConnection connection) +193
   System.Data.Entity.Infrastructure.<>c__DisplayClass1.<ResolveManifestToken>b__0(Tuple`3 k) +32
   System.Collections.Concurrent.ConcurrentDictionary`2.GetOrAdd(TKey key, Func`2 valueFactory) +72
   System.Data.Entity.Infrastructure.DefaultManifestTokenResolver.ResolveManifestToken(DbConnection connection) +180
   System.Data.Entity.Utilities.DbConnectionExtensions.GetProviderInfo(DbConnection connection, DbProviderManifest& providerManifest) +56
   System.Data.Entity.DbModelBuilder.Build(DbConnection providerConnection) +43
   System.Data.Entity.Internal.LazyInternalContext.CreateModel(LazyInternalContext internalContext) +62
   System.Data.Entity.Internal.RetryLazy`2.GetValue(TInput input) +123
   System.Data.Entity.Internal.LazyInternalContext.InitializeContext() +611
   System.Data.Entity.Internal.InternalContext.GetEntitySetAndBaseTypeForType(Type entityType) +18
   System.Data.Entity.Internal.Linq.InternalSet`1.Initialize() +53
   System.Data.Entity.Internal.Linq.InternalSet`1.GetEnumerator() +15
   System.Data.Entity.Infrastructure.DbQuery`1.System.Collections.Generic.IEnumerable<TResult>.GetEnumerator() +53
   System.Collections.Generic.List`1..ctor(IEnumerable`1 collection) +369
   System.Linq.Enumerable.ToList(IEnumerable`1 source) +58
   XXXWebsite.Controllers.YYYController.List() +21
   lambda_method(Closure , ControllerBase , Object[] ) +62
   System.Web.Mvc.ActionMethodDispatcher.Execute(ControllerBase controller, Object[] parameters) +14
   System.Web.Mvc.ReflectedActionDescriptor.Execute(ControllerContext controllerContext, IDictionary`2 parameters) +157
   System.Web.Mvc.ControllerActionInvoker.InvokeActionMethod(ControllerContext controllerContext, ActionDescriptor actionDescriptor, IDictionary`2 parameters) +27
   System.Web.Mvc.Async.AsyncControllerActionInvoker.<BeginInvokeSynchronousActionMethod>b__36(IAsyncResult asyncResult, ActionInvocation innerInvokeState) +22
   System.Web.Mvc.Async.WrappedAsyncResult`2.CallEndDelegate(IAsyncResult asyncResult) +29
   System.Web.Mvc.Async.WrappedAsyncResultBase`1.End() +49
   System.Web.Mvc.Async.AsyncControllerActionInvoker.EndInvokeActionMethod(IAsyncResult asyncResult) +32
   System.Web.Mvc.Async.AsyncInvocationWithFilters.<InvokeActionMethodFilterAsynchronouslyRecursive>b__3c() +50
   System.Web.Mvc.Async.<>c__DisplayClass45.<InvokeActionMethodFilterAsynchronouslyRecursive>b__3e() +225
   System.Web.Mvc.Async.<>c__DisplayClass30.<BeginInvokeActionMethodWithFilters>b__2f(IAsyncResult asyncResult) +10
   System.Web.Mvc.Async.WrappedAsyncResult`1.CallEndDelegate(IAsyncResult asyncResult) +10
   System.Web.Mvc.Async.WrappedAsyncResultBase`1.End() +49
   System.Web.Mvc.Async.AsyncControllerActionInvoker.EndInvokeActionMethodWithFilters(IAsyncResult asyncResult) +34
   System.Web.Mvc.Async.<>c__DisplayClass28.<BeginInvokeAction>b__19() +26
   System.Web.Mvc.Async.<>c__DisplayClass1e.<BeginInvokeAction>b__1b(IAsyncResult asyncResult) +100

The error message contains this: Unable to locate a Local Database Runtime installation.

Is this because LocalDB is not supported in Winhost?